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OF  THE 


***** NOV14j91» 

Accessions  No.     % w .V  Book  No.-.. 


LOWER  DIVISION 


• 
i 


SCIENTIFIC  MEMOIES 


EDITED    BY 


J.  S.  AMES,  PH.D. 

PKOFESSOB  OF   PHYSICS   IN   JOHNS    HOPKINS    UNIVERSITY 


XIV 

THE  EXPANSION  OF  GASES  BY  HEAT 


THE  EXPANSION  OF  GASES 
BY  HEAT 


MEMOIRS  BY  DALTON,  GAY-LUSSAC,  REGNAULT 
AND   CHAPPU1S 


TRANSLATED    AND    EDITED    BY 

WYATT  W.  RANDALL,  PH.D. 

HEADMASTER  OF  THE  MACKENZIE  SCHOOL,  DOBBS  FERRY,  N.   Y. 


NEW  YORK  •:-  CINCINNATI  •:-  CHICAGO 

AMEEICAN  BOOK  COMPANY 


COPYRIGHT,  1902,  BY 
AMERICAN  BOOK  COMPANY. 


Entered  at  Stationers'1  Hall,  London, 

Expansion  of  Gases. 
W.  P.  I 


PEEFATOEY  NOTE. 

IN  preparing  a  volume  to  contain  the  classical  memoirs 
which  treat  of  the  law  of  the  expansion  of  gases  by  heat,  a 
choice  which  will  be  satisfactory  from  all  points  of  view  can 
scarcely  be  expected.  The  memoirs  of  Dalton,  Gay-Lussac  and 
Regnault  are  of  course  given  in  full;  were  it  not  for  the  very 
comprehensive  abstract  given  in  Regnault's  first  paper,  the 
memoirs  of  Rudberg  would  certainly  have  been  included.  It 
has  seemed  best  to  the  editor  not  to  print  in  full  any  other 
than  the  memoirs  mentioned  ;  all  others  of  sufficient  import- 
ance are  referred  to  in  the  historical  Introduction.  An  excep- 
tion has  been  made,  however,  in  the  case  of  Chappuis's  research, 
for  the  proper  comprehension  of  which  a  fuller  abstract  was 
needed  than  could  readily  be  included  in  the  Introduction. 
This  abstract  is  therefore  given  separately. 

The  Bibliography  contains,  along  with  a  few  others  closely 
connected,  a  list  of  the  memoirs  printed  in  full  or  discussed  in 
the  Introduction. 

DOBBS  FERRY,  NEW  YORK. 


GENERAL    CONTENTS. 

PAGE. 
Prefatory  Note        .......         v 

Introduction  .  .  .  .  .  .  .3 

On  the  Expansion  of  Gases  by  Heat.    By  John  Dalton        .        17 
Extract  f rom  "  A  New  System  of  Chemical  Philosophy." 

By  John  Dalton        ......        22 

Biographical  Sketch  of  Dalton    .....        22 

Researches    upon    the   Rate  of  Expansion  of  Gases   and 

Vapors.    By  L.  J.  Gay-Lussac      .  .  .  .25 

Biographical  Sketch  of  Gay-Lussac        .  .  .  .48 

The  Determination  of  the  Rate  of  Expansion  of  Gases  by 
Heat.    An  extract  from  the  "  Traite  de  Physique  " 
of  J.  B.  Biot  ......        51 

Researches  upon  the  Rate   of  Expansion  of  Gases.    First 

Memoir.     By  H.  V.  Regnault        ....        63 

Biographical  Sketch  of  Regnault  .  .  .  .120 

Researches  upon  the  Rate  of  Expansion  of  Gases.    Second 

Memoir.     By  H.  V.  Regnault        .  .  .  -    — .      121 

Researches  upon  the  Gas  Thermometer,  and  the  Compari- 
son of  the  Gas  Thermometer  with  the  Mercury  Ther- 
mometer.   By  P.  Chappuis.    Abstract  .  .  .151 
Bibliography            .......      159 

Index  .  .  .  161 


vn 


INTRODUCTION. 


CONTENTS. 


PAGE 

Dalton          .         .........         3 

Gay-Lussac          .        .        .        .        .        .        ..       N.        .        3 

Dulong  and  Petit        .     '    .  •      '.         ...         •  -  \  •         •         4 

Flaugergues         .    .    --.••       .        .        .        -.'".'      .        .        5 
Rudberg       .  .        .        ,        ^        .        .        .        .        5 

Magnus .        s        .        6 

Regliault      .        r^  w  .        .        .        .        .        ....         7 

Balfour  Stewart  .        .        .        .        .        . ,       .        .        9 

Recknagel     .        .'       ....        .        ,        .        ...        9 

v.  Jolly         .     '  ,        .        .        .        ,        .        .  •     .        .        9 
Amagat        .        .         .         .         .         .         ,         .         .         .10 

Mendeleeff  and  Kajander    .        .         .  .        .        .       11 

Andrews      .         .         .  .         .         .  .         .12 

Callendar  and  Griffiths       .         .         .         ,         .         .         .       13 

Chappuis  and  Harker          . 13 

Wiebe  and  Bottclier      .        .        .  .        .        .        .13 

Kuenen  and  Randall  .        .  .         .         .         .14 

Melander .        .         .14 

Baly  and  Ramsay 15 


INTEODUCTION. 

THE  Law  of  the  Expansion  of  Gases  by  Heat,  variously 
called  the  Law  of  Charles,  Dalton,  and  Gay-Lussac,  seems  to 
have  been  for  the  first  time  definitely  made  known  to  the 
scientific  world  by  the  English  chemist.  As  Roscoe  says, 
"  This  law  of  equal  expansion  of  all  gases  for  equal  increments 
of  temperature  has  been  generally  known  on  the  Continent  as 
*  Gay-Lussac's  '  or  '  Charles's  law,'  but  ought  to  be  called  l  Dai- 
ton's  law  of  expansion, 'as  he  first  announced  it  and  gave  experi- 
mental evidence  of  its  truth,  and  the  claims  of  the  Manchester 
philosopher  are  generally  now  allowed/'  (John  Dalton,  and  the 
Rise  of  Modern  Chemistry,  page  96.) 

The  experimental  basis  upon  which  Dalton  founded  his 
generalization  was,  however,  meagre  and,  from  a  modern  stand- 
point, quite  inaccurate — as  was  the  case  also  with  the  evidence 
upon  the  strength  of  which  he  put  forth  his  Law  of  Multiple 
Proportions  and  the  original  Atomic  Hypothesis.  The  work 
done  upon  this  subject  by  Dalton  and  Gay-Lussac — and  es- 
pecially by  the  latter, — the  results  of  which  were  published  in 
1802,  forms  an  epoch  in  the  history  of  the  careful  study  of  the 
properties  of  gases,  if  for  no  other  reason  than  because  of  the 
recognition  of  the  necessity  for  the  thorough  removal  of  water 
vapor  from  the  gas  examined,  before  concurrent  results  could 
be  expected. 

Of  the  investigations  carried  out  prior  to  the  beginning  of 
the  Nineteenth  Century,  Gay-Lussac  gives  a  sufficient  account 
in  his  first  memoir.  During  the  year  1801  Dalton  read  a  series 
of  papers  before  the  Manchester  Society,  one  of  which  treated 
of  the  rate  of  expansion  of  air  and  other  gases  and  records,  as 
its  author  states,  experiments  undertaken  to'  test  the  results  of 
the  research  of  Guyton  de  Morveau  and  Duvernois.  On 
account  of  its  bearing  upon  certain  theories  which  he  held 
upon  the  nature  of  heat,  Dalton's  attention  was  especially 
drawn  to  the  increase  in  the  rate  of  expansion  with  rise  of 

3 


MEMOIRS    ON 

temperature,  and  he  does  not  seem  to  have  calculated  an  aver- 
age coefficient  of  expansion  on  the  basis  of  the  volume  of  the 
gas  at  the  melting-point  of  ice,  from  the  results  of  these  experi- 
ments. After  the  publication  of  Gay-Lussac's  research,  how- 
ever, he  apparently  repeated  his  experiments  with  greater  care, 
using  32° F.  as  one  limit  of  the  temperature-range,  and  calcu- 
lated from  the  results  thus  obtained  the  coefficient  which  in  his 
"New  System"  he  states  was  the  same  as  that  announced  by 
Gay-Lussac.  This  matter  is  discussed  in  a  footnote  on  page 
72.  Dalton's  first  paper  was  published  before  that  of  the 
French  savant,  but  in  all  probability  not  until  the  latter's  ex- 
perimental work  had  been  completed. 

It  is  singular  that  Gay-Lussac's  later  and,  apparently  in  his 
opinion,  more  accurate  investigation, — an  account  of  which  is 
given  in  the  form  of  an  extract  from  Biot's  Traite  de  Physique 
— should  have  been  made  known  to  the  world  only  through 
this  means. 

The  results  of  the  profound  researches  of  Dulong  and  Petit 
upon  the  absolute  expansion  of  mercury  and  the  relation  be- 
tween the  mercury  and  gas  scales  of  temperature,  were  to  a 
certain  extent  vitiated  through  their  apparent  acceptance  of 
the  Gay-Lussac  coefficient  0.00375  for  the  expansion  of  air0 
One  at  least  of  their  own  experiments  pointed  to  a  figure  much 
nearer  that  now  accepted  as  correct,  but  such  evidence  as  now 
exists  indicates  the  use  of  the  higher  value  in  their  computa- 
tions. Their  method  involved  the  use  of  an  open  air-ther- 
mometer whose  tip  was  sealed  after  it  had  been  heated  to  some 
definite  temperature;  after  the  apparatus  had  been  allowed  to 
cool  again  to  0°,  the  tip  of  the  thermometer  tube  was  again 
opened  under  mercury  and  from  the  Amount  of  mercury 
drawn  in  the  expansion  of  the  air  at  the  previous  high  temper- 
ature was  calculatedo  Practically  the  same  method  was  after- 
wards employed  by  Rudberg  and  by  Regnault  in  their  researches 
upon  the  rate  of  expansion  of  gases.  Assuming  the  coefficient 
Oo 00375  for  air  and  calculating  on  this  basis  the  true  tempera- 
tures registered  by  their  air  thermometers,  Dulong  and  Petit 
naturally  found  greater  deviation  from  the  air  standard  on  the 
part  of  mercury  than  the  more  accurate  work  of  Regnault  and 
others  has  since  proved  to  exist.  Since  the  coefficient  of  ex- 

4 


EXPANSION     OF    GASES 

pansion  of  mercury  found  by  them  has  been  shown  by  more 
recent  investigations  to  be  very  nearly  exact,  it  remains  but  to 
substitute  the  correct  value  for  the  coefficient  of  expansion  of 
air  to  determine,  with  only  slight  error,  the  actual  deviation  of 
the  mercury  scale  from  the  air  scale  of  temperature. 

In  Gehler's  Physikalisches  Worterbuch  (1825)  an  account  is 
given  of  two  researches  upon  the  rate  of  expansion  of  air  by 
H.  Flaugergues,  published  in  the  Journal  de  Pharmacie. 
Using  a  glass  flask  similar  to  that  employed  by  Gay-Lussac  in 
his  earlier  experiments,  he  found  0.371168  for  the  amount  of 
the  expansion  of  unit  volume  of  air  between  0°  and  80°  R»  If 
allowance  must  be  made  for  the  expansion  of  the  flask,  this 
fraction  becomes  0.375671 — nearly  the  same  as  Gay-Lussac's. 
It  is  not  clear  from  the  context  that  Flaugergues  took  the 
expansion  of  the  flask  into  account  ;  nevertheless  it  is  likely, 
and  the  coefficient  first  given,  0.00371,  is  probably  his  corrected 
resulto  The  fact  of  the  expansion  of  the  containing  vessel  was 
at  that  time  well  known  and  generally  allowed  for  ;  besides,  in 
the  experiments  described  in  the  second,  paper  the  author 
made  use  of  a  method  intended  to  eliminate  this  factor :  the 
gas  was  contained  in  a  cylindrical  glass  vessel  in  which  was  a 
smaller  leaden  cylinder ;  the  greater  rate  of  expansion  of  the 
lead  was  to  bring  about  a  decrease  of  the  vessel's  capacity  for 
gas  exactly  compensating  for  the  increase  in  the  size  of  the 
glass  envelope.  These  experiments  led  to  the  figure  0.37174 
for  the  amount  of  the  expansion  between  0°  and  80°  R. — 
practically  identical  with  the  former  result.  An  experiment 
with  moist  air  yielded  as  a  result  0.411. 

The  determinations  of  Flaugergues  seem  to  have  attracted 
little  attention,  and,  although  they  had  pointed  out  the  possi- 
bility of  error  in  Gay-Lussac's  coefficient,  it  was  not  until  the 
publication  of  the  very  noteworthy  memoirs  of  Rudberg  that 
the  matter  received  due  consideration. 

In  the  course  of  an  investigation  which  had  for  its  object  the 
accurate  determination  of  the  melting  points  of  the  metals 
lead,  tin  and  antimony  on  the  scale  of  the  air  thermometer, 
Rudberg  had  found  that,  assuming  Gay-Lussac's  coefficient 
0,00375  to  be  correct,  he  was  led  to  conclude  that  the  coefficient 
of  expansion  of  glass  was  far  greater  at  high  temperatures  than 

5 


ME  MO  IBS    ON 

its  behavior  at  ordinary  temperatures  would  appear  to  promise. 
He  accordingly  undertook  the  re-determination  of  the  air 
coefficient,  employing,  first,  a  method  in  which  both  volume 
and  pressure  varied,  and,  second,  one  in  which  the  volume 
remained  constant.  The  original  memoirs  are  not  given  in 
the  form  of  translation  in  this  volume,  as  a  sufficient  abstract 
of  them  is  given  by  Regnault  in  his-  first  paper. 

It  will  be  well,  in  passing,  to  call  attention  to  the  fact  that  the 
first  method  of  experiment  employed  by  Rudberg  was  that 
which  had  been  used  previously  by  Dulong  and  Petit,  but  that 
the  second  seems  to  have  been  original  with  him  ;  except  for 
comparatively  slight  modifications  intended  to  secure  greater 
accuracy,  the  constant-volume  air  thermometer  of  to-day  is  the 
invention  of  Rudberg. 

Both  methods  of  determination  led  to  the  same  result  :  Gay- 
Lussac's  coefficient  is  too  high  by  about  one  part  in  thirty-seven  ; 
the  figure  adopted  by  Rudberg  as  the  probable  coefficient  of 
expansion  of  air  is  "between  0.00364  and  0.00365."  It  had 
been  his  intention  to  investigate  other  gases  as  well,  but  his 
death  occurred  shortly  after  the  publication  of  the  results 
obtained  for  air. 

The  great  importance  of  the  question  involved  was  generally 
recognized  and,  consequently,  within  about  four  years  the 
results  of  two  careful,  quite  independent,  investigations,  one 
by  Magnus  in  Berlin,  the  other  by  Regnault  in  Paris,  made 
their  appearance.  While  neither  of  them  was  led  to  a  figure 
for  the  air  coefficient  quite  so  low  as  that  adopted  by  Rudberg, 
both  were  able  to  support  the  latter's  contention  that  the 
coefficient  found  by  Gay-Lussac  was  far  too  high.  It  is  interest- 
ing to  note,  however,  that  just  as  the  more  accurate  work  of 
Magnus  and  Regnault  showed  that  Rudberg's  coefficient  was  too 
low,  exactly  the  same  fate  has  befallen  the  coefficient  adopted 
by  Magnus  and  Regnault,  through  the  investigations  carried 
out  since  1860. 

Magnus— as  did  also  Regnault — endeavored  to  repeat  the 
later  experiments  of  Gay-Lussac  with  air  at  constant  pressure, 
but  found  it  impossible  to  secure  uniform  results,  evidently 
because  the  short  mercury  piston  failed  to  close  completely  the 
bore  of  the  thermometer  tube  :  air  leaked  in  or  out  according 

6 


EXPANSION     OF    OASES 

to  the  direction  of  movement  of  the  mercury  index  and  the 
relative  tension  within  and  without  the  tube.  Turning  to 
Rudberg's  second  method  :  that  by  which  the  increase  of 
pressure  within  a  gas  reservoir  of  constant  volume  was  measured 
instead  of  the  increase  in  the  volume  of  a  gas  kept  at  constant 
pressure  :  Magnus  obtained  eight  values  for  a  ranging  from 
0.00365032  to  0.00367899  with  a  mean  of  0.00366508 — at  a 
barometric  pressure  of  28  inches  ;  at  760  mm.  pressure  this 
mean  value  becomes  0.0036678.  At  28  inches  pressure  the 
mean  coefficient  found  for  hydrogen  was  0.00365659  ;  for  car- 
bon dioxide,  0.00369087 ;  for  sulphur  dioxide,  0.00385618, 
While  the  mean  value  for  air  found  by  Magnus,  after  recalcula- 
tion for  a  pressure  of  760  mm.,  is  nearer  than  is  the  mean 
value  found  by  Regnault  by  his  four  different  methods,  to  the 
coefficient  for  constant  volume  now  accepted,  this  fact  cannot 
be  interpreted  as  a  proof  of  greater  accuracy  of  experimental 
work  on  the  part  of  the  German  physicist.  Regnault's  lowest 
result  was  0.0036549,  and  highest  0.0036747— a  range  of 
0.0000198  in  fifty  determinations  carried  out  by  four  distinct 
methods  ;  for  any  one  method  the  range  amounted  to  but  two 
thirds  of  this  amount,  at  the  most.  On  the  other  hand, 
Magnus's  results,  all  by  one  method  and  only  eight  in  number, 
ranged  0.00002867.  For  hydrogen  the  range  from  highest  to 
lowest  was  0.0000029  in  four  determinations  ;  for  carbon  dioxide, 
0.00002228  in  four ;  for  sulphur  dioxide,  0.00006552  in  three 
determinations. 

Magnus  suggests  as  a  possible  explanation  of  the  difference 
between  the  results  of  Gay-Lussac  and  those  of  Rudberg  and 
himself,  among  other  things,  the  fact  that  the  former's  gas 
reservoir  was  actually  in  the  boiling  water  of  the  bath  instead 
of  in  its  vapor. 

Regnault's  two  memoirs  on  the  expansion  of  gases  are  given 
in  full  in  the  form  of  a  translation.  It  is  to  be  noted  that  he 
employed  with  success  five  different  forms  of  apparatus  to 
determine  this  expansion  between  0°  and  100°  :  in  the  first  of 
these  both  volume  and  pressure  varied  to  a  considerable  degree  ; 
in  the  second  the  volume  remained  more  nearly  constant ;  in  the 
third  and  fourth  the  volume  changed  only  to  the  extent  of  the 
expansion  of  the  glass  envelope  ;  while  in  the  fifth  the  increase 

7 


MEMOIRS    ON 

of  volume  was  directly  determined  under  constant  pressure. 
The  last  mentioned  method  established  the  fact  that  for  most 
gases  the  coefficient  of  expansion  at  constant  pressure  is  slightly 
greater  than  that  at  constant  volume,  because  such  gases  do 
not  exactly  conform  to  Boyle's  Law,  but  contract  more  rapidly 
in  proportion  than  the  pressure  upon  them  increases.  Thus 
the  mean  value  found  for  air  at  constant  volume  is  stated  by 
Regnault  to  be  0.003665,  and  that  for  constant  pressure, 
0.0036706, — at  about  atmospheric  pressure.  The  latter  coeffi- 
cient increases  as  the  pressure  is  increased  :  at  about  3£  atmos- 
pheres it  is  between  0.00369  and  0.00370. 

Both  Magnus  and  Regnault  then  proceeded  independently  to 
re-determine  the  variation  between  the  mercury  scale  and  the 
air  scale  of  temperature.  Since  the  data  showing  the  dimen- 
sions of  the  apparatus  of  Dulong  and  Petit  were  unknown,  it 
was  impossible  with  certainty  to  re-calculate  their  results  with 
the  aid  of  a  more  nearly  correct  coefficient  of  expansion  for  air. 
Gay-Lnssac  had  declared  that  air  and  mercury  expand  pro- 
portionally even  at  comparatively  high  temperatures  ;  Dulong 
and  Petit  found  in  their  research  that  soon  after  passing  100° 
mercury  began  to  expand  more  rapidly,  and  that  at  about  300° 
the  temperature  by  the  mercury  scale  was  over  7°  higher  than 
that  calculated  from  the  readings  of  their  air  thermometer. 

Here,  again,  the  superiority  of  the  experimental  work  of 
Regnault  cannot  be  questioned.  It  established  the  fact  that 
the  air  thermometers  and  the  mercury  thermometers  agree  up  to 
about  250°  ;  above  this  point  mercury  expands  more  rapidly  in 
proportion  than  air,  and  at  350°  (by  the  air  thermometer)  the 
mercury  thermometer  stands  about  3  °  higher. 

Magnus's  work,  on  the  other  hand,  led  to  the  practical  con- 
firmation of  the  results  of  Dulong  and  Petit.  As  Magnus  had 
used  the  coefficient  0.003665  (at  28  inches  ;  0.0036678  at  760 
mm.)  in  calculating  his  air  thermometer  temperatures,  he  was 
led  to  believe  that  Dulong  and  Petit  had  not  after  all  made  use 
of  Gay-Lussac's  coefficient,  but  that,  having  in  a  single  inde- 
pendent determination — as  was  known — found  the  coefficient 
0.00365,  they  had  employed  the  latter  instead.  This  sup- 
position Regnault,  in  criticizing  Magnus's  results,  considered 
extremely  unlikely,  on  the  ground  that  a  study  of  Dulong  and 

8 


EXPANSION     OF    OASES 

Petit's  results  does  not  seem  at  all  to  confirm  it,  and  that  the 
latter  would  hardly  have  depended  upon  a  single  determination 
of  so  important  a  factor,  especially  when  so  at  variance  with 
the  generally  accepted  figure  of  Gay-Lussac.  Into  the 
criticisms  passed  upon  one-another's  apparatus  there  is  no  need 
here  to  go. 

An  investigation  of  the  behavior  of  gas  thermometers  at 
about  — 88°  led  Eegnault  to  the  conclusion  that  the  coefficients 
of  expansion  for  air  and  hydrogen  preserve  closely  the  ratio 
shown  at  higher  temperatures. 

In  his  comparison  of  the  various  gas  thermometers  in  the 
Memoires  of  the  Academy  of  Sciences,  Regnault  speaks  of  using 
a  coefficient  for  hydrogen  smaller  than  he  records  in  any  of  his 
experiments.  Lord  Kelvin  has  called  attention  to  the  fact  that 
this  statement  is  probably  in  error  (See  Encyclopedia  Britan- 
nica,  article  "Heat"). 

Mention  may  be  made  here,  finally,  of  the  study  by  Regnault 
of  the  coefficient  of  expansion  of  gases  under  high  pressures, 
the  results  of  which  are  contained  in  a  later  volume  of  the 
Memoires. 

The  accuracy  of  the  results  of  Regnault  for  air  at  constant 
volume  was  put  to  the  test  by  Recknagel  and,  still  more  rigor- 
ously, by  Balfour  Stewart  ;  the  results  of  the  former  confirmed 
those  of  Magnus,  so  far  as  the  value  of  the  coefficient  is  con- 
cerned, Recknagel's  mean  value  being  0.0036681.  Stewart,  like 
Recknagel,  used  the  method  employed  successfully  by  Rudberg, 
Magnus  and  Regnault  to  find  the  coefficient  of  expansion  from 
the  rise  of  tension  in  a  gas  kept  at  constant  volume  while  its 
temperature  rises,  but,  using  even  greater  care  than  did  any  of 
his  predecessors  to  secure  pure  dry  air  for  his  apparatus,  and 
employing  every  known  refinement  in  the  measurement  of  the 
pressure  changes,  he  obtained  the  figure  0.0036728  as  the 
average  of  four  results,  the  highest  of  which  was  0.0036739  and 
the  lowest,  0.0036716. 

The  results  recorded  in  the  memoir  of  v.  Jolly,  although 
scarcely  to  be  compared  as  regards  accuracy  with  those  of 
Stewart,  are  interesting  because  of  the  author's  success  in 
simplifying  the  constant-volume  gas  thermometer.  The  differ- 
ences between  his  highest  and  lowest  results  were,  how- 
B  9 


MEMOIRS    ON 

ever,  not  so  great  as  those  between  the  corresponding  figures 
in  the  several  series  of  Regnaolt's  determinations.  He  was  also 
successful  in  determining  the  coefficient  of  expansion  of  oxygen, 
which  Regnault  had  failed  to  do.  For  air,  v.  Jolly  found  in  20 
experiments:  highest,  0.0036724;  lowest,  0.003665;  mean, 
0.00366957.  For  oxygen  (18  experiments)  the  highest  was 
0.003680  ;  lowest,  0.0036683  ;  mean,  0.0036743.  For  hydrogen, 
the  highest  of  4  results  was  0.0036600  ;  lowest,  0.0036530  ; 
mean,  0.0036562.  For  nitrogen,  the  highest  of  4  results  was 
0.0036717  ;  lowest,  0.0036655  ;  mean,  0.01/36677.  For  carbon 
dioxide,  the  highest  of  17  results  was  0.0037144  ;  lowest, 
0.0036962  ;  mean,  0.0037060. 

Of  the  extensive  and  important  researches  of  Amagat  one 
memoir  and  part  of  another  have  appeared  in  the  form  of  a 
translation  in  an  earlier  volume  of  this  series — "  The  Laws  of 
Gases  :  Memoirs  by  Boyle  and  Amagat."  Earlier  than  either 
of  these  is  a  study  (1873)  of  the  variation  of  the  coefficient  of 
expansion  of  gases  with  rise  of  temperature  ;  a  constant-vol- 
ume method  based  upon  that  of  Rudberg  was  employed. 
Assuming  that  for  air  the  mean  value  of  a  ==  0.00367  between 
0°  and  100°,  he  finds  the  mean  values  of  a  for  sulphur  dioxide 
and  carbon  dioxide  steadily  decrease  as  the  temperature  rises. 
Thus,  for  the  former  gas  it  is  0.003904  between  10°  and  60°, 
but  0.003798  between  10°  and  250°;  between  0°  and  10°  it  is 
0.00413,  at  25°  0.00394,  at  100°  0.003757,  at  250°  0.003685. 
For  carbon  dioxide  the  mean  value  of  a  between  0°  and  50°, 
is  0.003714;  between  0 °  and  250° ,  0.0037028;  at  0  °it  is  0.003724; 
at  50°,  0.003704;  at  100°,  0.003695;  at  250°,  0.003682. 

From  the  memoir  of  1881,  the  following  may  be  quoted  with 
regard  to  the  behavior  of  gases  under  high  pressures: 

"1.  The  coefficient  of  expansion  of  gases  {referred  to  unit 
volume)  increases  with  the  pressure  up  to  a  maximum  value, 
beyond  which  it  decreases  indefinitely. 

"  2.  The  maximum  occurs  at  a  pressure  for  which  the  pro- 
duct^ is  a  minimum;  consequently  at  this  point  the  gas  acci- 
dentally obeys  Marietta's  law. 

"  3.  For  continually  rising  temperatures  this  maximum  be- 
comes less  and  less  distinct  and,  finally,  disappears." 

Hydrogen  even  at  very  low  pressures  seems  already  to  have 

10 


EXPANSION     OF    GASES 

passed  the  point  where  ^  is  a  minimum;  hence  its  coefficient 
constantly  decreases  as  pressure  rises  and  as  temperature  rises. 
The  pressures  employed  in  these  experiments  ranged  from  40 
to  320  metres  of  mercury. 

In  a  later  memoir  (1893)  are  recorded  results  obtained 
through  a  still  greater  range  of  pressures.  Amagat  says,  "  An 
inspection  of  Table  21  shows  that  at  the  outset  the  coefficient 
of  expansion  increases  with  the  pressure,  as  Regnault  had 
already  found  for  pressures  of  a  few  atmospheres  ;  it  then 
passes  through  a  maximum  which  occurs  at  a  pressure  rising 
regularly  with  the  temperature.  During  my  first  researches 
on  this  subject  these  maxima  seemed  to  coincide  with  those 
pressures  for  which  the  product  pv  is  a  mimimum;  but  the 
more  extended  data  of  the  present  memoir  show  this  law  to  be 
only  approximate."  With  rise  of  pressure  from  1000  to  3000 
atmospheres,  the  coefficient  of  expansion  of  oxygen  between  0° 
and  16°  steadily  decreased  from  0.00236  to  0.00134,  that  of 
hydrogen  from  0.00200  to  0.00128,  that  of  nitrogen  from 
0.00193  to  0.00098,  and  that  of  air  from  0.00206  to  0.00110. 
Another  series  of  experiments  showed  that  with  rise  of  pressure 
from  200  to  1000  atmospheres  a  similar  fall  in  the  value  of  the 
coefficient  was  to  be  noted.  The  coefficient  in  the  case  of  car- 
bon dioxide  rises  to  a  maximum  and  decreases;  this  maximum 
occurs  at  higher  and  higher  pressures  as  the  temperature  rises: 
thus,  at  137°— 198°,  a  is  0.00369  (of  the  volume  at  137°  con- 
sidered as  unity)  when  the  pressure  is  75  atmospheres;  0.00798 
(maximum  value)  at  200  atmospheres,  0.00386  at  500,  and 
0.00223  at  900  atmospheres.  The  coefficient  of  carbon  dioxide 
for  constant  pressure  rises  at  first  with  the  temperature,  passes 
a  maximum,  and  then  decreases  as  temperature  rises;  as  the 
pressure  is  higher,  the  maximum  occurs  at  higher  and  higher 
temperatures. 

The  elaborate  investigations  of  Mendeleeff  upon  the  proper- 
ties of  gases  are  to  a  large  extent  a  terra  ignota  for  those  who 
cannot  read  Russian  ;  only  a  few  papers,  usually  meagre  ab- 
stracts, contained  in  journals  published  in  Western  Europe,  are 
available  as  sources  of  information.  In  papers  published  in 
conjunction  with  Kajander,  he  discussed  the  disadvantages  of 
Regnault's  constant-pressure  method,  among  others  that  only 

11 


MEMOIRS    ON 

about  two  thirds  of  the  gas  contained  in  the  apparatus  was  at 
the  temperature  of  the  water  vapor.  In  fact,  in  his  Princi- 
ples of  Chemistry  (2nd  Edition,  Volume  1,  page  133,  note), 
he  goes  so  far  as  to  state  "  Regnault,  however,  did  not  directly 
determine  the  change  of  volume  between  0°  and  100°,  but 
measured  the  variation  of  tension  with  the  change  of  tempera- 
ture; but  since  gases  do  not  entirely  follow  Mariotte's  law,  the 
change  of  volume  cannot  be  directly  judged  by  the  variation 
of  tension."  Nine  results  obtained  with  an  apparatus  in  which 
the  entire  volume  of  gas  was  surrounded  with  water  vapor,  and 
various  devices  were  employed  to  increase  the  accuracy  of  the 
readings,  ranged  from  0.0036814  to  0.0036876,  with  a  mean  of 
0.0036843.  This  is  the  coefficient  of  expansion  of  air  at  a  con- 
stant pressure  of  about  760  mm.;  the  probable  error  of  the 
mean  value  is  estimated  by  Mendeleeff  to  be  0.0000005. 

In  his  Principles  of  Chemistry  Mendeleeff  gives  the  results 
obtained  at  constant  volume:  for  air,  0.00368;  for  hydrogen, 
0.00367;  for  carbon  dioxide,  0.00373;  for  hydrobromic  acid 
gas,  0.00386.  At  3£  atmospheres  pressure  a  becomes  0.00371 
in  the  case  of  air.  The  coefficient  of  expansion  of  carbon 
dioxide  rises  with  pressure  as  follows  :  at  1  atmosphere,  0.00373; 
at  3,  0.00389;  at  8  atmospheres,  0.00413.  In  the  case  of  hydro- 
gen which  is,  on  the  other  hand,  less  compressible  than  Boyle's 
Law  would  lead  one  to  expect,  the  rise  of  the  coefficient  with 
increase  of  pressure  is  slower:  at  one  atmosphere  it  is  0.00367; 
at  eight  atmospheres,  0.00369. 

In  one  paper  Mendeleeff  recalculates  the  results  of  Magnus, 
Regnault  and  v.  Jolly  for  air  at  constant  volume,  reducing  the 
barometric  readings  to  45°  latitude.  He  gives  the  following 
table: 

Determinations  As  given  by  author  Corrected  value. 

Magnus  8  0.0036651  0.0036700 

Regnault  15  0.003665  0.0036694 

v.  Jolly  20  0.0036696  0.0036702 

Mean,  0.003670 

The  coefficient  for  constant  pressure,  as  found  by  himself 
with  Kajander,  is  recalculated  in  the  same  way  and  given  as 
0.003681. 

The  investigations  of  Andrews  upon  the  critical  state, 

12 


EXPANSION     OF    GASES 

among  other  points,  led  to  a  study  of  the  coefficient  of  expan- 
sion of  carbon  dioxide  at  higher  pressures.  He  gives  the 
following  figures  for  a  (constant  pressure)  atO° — 7.5° : 

ftaSr^I        12         16'25      20'01        24'8        27'7         3L1       34'5 
Coefficient  0.00462    0.00520  0.00607  0.00700  0.00782  0.00895  0.01097. 

The  value  of  a  (64° -100°)  increases  with  increasing  pressure 
up  to  0.01822  at  145.5  atmospheres;  then  decreases:  at  223 
atmospheres,  a  =  0.0084. 

The  coefficient  for  constant  volume  rises  from  0.003526  at 
21-24  atmospheres  to  0.007018  at  94-118  atmospheres. 

Several  researches  conducted  during  the  past  fifteen  years 
have  shown  extraordinary  improvement  in  the  accuracy  of 
measurement  of  pressure  changes  in  gas  thermometers.  The 
researches  of  Callendar  upon  the  platinum  thermometer  and  its 
standardization  by  means  of  the  gas  thermometer,  have  led  to 
the  improvement  of  the  latter  as  an  instrument  for  exact 
determinations.  The  work  of  Cbappuis  is  so  striking  an 
example  of  the  kind  of  accuracy  referred  to,  that  a  much  more 
detailed  abstract  of  his  memoir  is  given  in  the  body  of  the 
book  (page  153).  The  coefficients  for  hydrogen  as  found  by 
him  are  :  constant  volume,  0.0036624  ;  constant  pressure, 
0.0036600.  If  these  are  reduced  to  their  limitary  values  which 
refer  to  zero  pressure,  they  become  0.0036624  and  0.0036625 
respectively,  giving  as  "absolute  zero  "on  the  centigrade  scale 
-273.04°.  The  mean  coefficient  of  expansion  found  by  him  for 
nitrogen,  at  constant  volume,  between  0°  and  100°  is 
0.00367466.  The  figure  found  for  air  by  Callendar  and  Grif- 
fiths is  almost  identical,  0.0036749.  The  latter  was,  however, 
the  result  of  but  a  single  determination.  Wiebe  and  Bottcher 
found  an  average  value  of  0.0036706  for  air,  in  a  series  of  figures 
ranging  from  0.0036694  to  0.0036713.  Finally,  Harker  and 
Chappuis,  in  a  recent  memoir,  find  as  the  coefficient  of  expan- 
sion of  nitrogen  at  constant  volume  (in  glass)  the  figure 
0.00367180  for  an  initial  pressure  of  793.5  mm.  of  mercury,  and 
0.0036683  for  an  initial  pressure  of  530.8  mm.  of  mercury.  In 
the  limit,  then,  at  zero  pressure,  it  would  be  0.0036613.  The 
limiting  value  for  the  coefficient  at  constant  pressure  is 
0.0036612.  These  results  indicate  the  limit  of  accuracy 
attained  up  to  this  time. 

13 


MEMOIRS    ON 


In  1895  Kuenen  and  Randall  examined  the  rate  of  expansion 
of  argon  and  helium  through  a  considerable  range  of  tem- 
perature ;  the  fact  that  the  coefficient  remained  almost  constant 
showed  the  absence  of  dissociation  in  the  gases  examined  and 
was  taken  as  proof  of  their  simple  molecular  condition. 

Before  closing,  reference  should  be  made  to  work  done  in 
tho  study  of  the  behavior  of  gases  at  very  low  pressures.  The 
results  of  the  research  of  Melander  are  summarized  in  the 
following  table,  where  p  =  initial  pressure,  p  =  final  pressure, 
a  =  coefficient  of  expansion  at  the  pressure  p' \  the  probable 
error  as  calculated  by  Melander,  is  given  for  the  first  and  last 
values  of  a  only,  these  being  the  limiting  values. 


P 

752 

376 

260 

170 

100 
78 
51.8 
29.1 
13.2 
6.6 


749 

254 

101 

75 

18.6 
5.8 


749 

347 

267 

169.5 

101.5 
55.8 
18.1 


764.5 
351.7 
191.0 
111.7 

48.4 

20.1 

9.3 


1027.7 

513.7 

355.2 

232.2 

136.6 

106.6 

70.8 

38.8 

18.1 

9.1 


I— AIR. 
a 

0.0036660 
6624 
6606 
6594 
6630 
6657 
6717 
6853 
7172 
7627 


II— AIR. 


1023.4 

346.9 

138.0 

102.5 

25.5 

7.98 


0.0036642 
6580 
6634 
6645 
6895 
7666 


III — CARBON  DIOXIDE. 


102S.1 

474.9 

365.2 

231.7 

138.7 

76.2 

24.7 


0.0037264 
6856 
6803 
6701 
6657 
6641 
6753 


IV — HYDROGEN. 


1043.6 

480.1 

260.8 

152.5 

66.2 

27.4 

12.8 


0.0036504 
6518 
6547 
6548 
6595 
6721 
7002 

14 


Error 
0.0000005 


0.0000021 
0.0000004 

0.0000021 
0.0000005 

0.0000015 
0.0000002 

0.0000022 


EXPANSION     OF    GASES 

It  will  be  noted  that  with  decrease  of  pressure  the  value  of  a 
falls  until  a  minimum  is  reached  and  then  rises  again  ;  with 
hydrogen,  on  the  one  hand,  the  minimum  seems  to  have  been 
reached  at  about  atmospheric  pressure  ;  with  air  the  minimum 
occurs  at  about  300  mm.  pressure,  and  with  carbon  dioxide  at 
about  100  mm. 

The  accuracy  of  the  results  obtained  by  other  experimenters 
at  very  low  pressures,  has  been  challenged  by  Baly  and  Earn- 
say,  who  point  out  the  difficulty  of  the  removal  of  all  gas  from 
a  glass  vessel  and  the  likelihood  of  the  presence  in  the  gas 
examined  of  carbon  dioxide  and  water  vapor  given  off  from 
the  walls  of  the  vessel  after  the  pressure  has  been  lowered.  The 
shrinkage  of  the  vessel  under  atmospheric  pressure  after  the 
removal  of  most  of  the  gas  contained  in  it,  is  another  source  of 
serious  error.  Of  course  these  difficulties  become  important 
only  at  very  low  pressures.  The  following  table  contains  the 
figures  found  for  the  coefficients  of  expansion  of  hydrogen, 
oxygen  and  nitrogen  at  pressures  below  5.5  mm.  : 

I  —  Hydrogen. 

Pressure  in  mm.  4.7  3.47  0.25  0.096  0.077 

-f    277T.S          ST^.T?  1T7S  5^7  THlW 

(0.003656    0.003653      0.003623       0.003366       0.003327 

II  —  Oxygen. 

Pressure  in  mm.  5.1        5.3        4.0  2.5  1.4         0.083         0.07 

4    ?^T        *^tf       *&*         ?^T   SsV.T       T^TT         ?l?         ??V.3" 
(0.0038310.0038460.003817    0.0039840.003998    0.004292    0.004098    0.004161 

III  —  Nitrogen. 

Pressure  in  mm.  5.3  4.97  3.0  1.1  0.8 

Coefficient 


0.003290      0.003238      0003315      0.003290    0.003021 
Pressure  in  mm.    0.6  0.6  0.6  0.6 

*ks  *&,  *  377  dfTT  THfT  *$?  37T  T^S 

0.0028170.002911     0.0026530.003096    0.0033220.003058    0.0026950.002915 

Mean    of  eight    results  at    0.6  mm.  =  7¥J.5T*  [=0.002919]. 

Baly  and  Ramsay  give  their  results  in  common  fractions  ;  the 

corresponding  decimal  fractions   have  been  introduced  for  the 

15 


EXPANSION     OF     GASES 

sake  of  comparison  with  the  results  of  others.  The  authors 
sum  up  their  results  as  follows  : 

"1.  The  coefficient  of  expansion  of  hydrogen  with  tem- 
perature decreases  as  pressure  is  lowered.  It  is  normal  down 
to  a  pressure  of  0.1  mm. 

"  2.  The  coefficient  of  expansion  of  oxygen  is  greater  than  the 
normal  one,  being  ^-^  instead  of  ^3  ;  it  increases  with  decrease 
of  pressure  to  ^^  at  1.4  mm.  ;  at  0.7  mm.  of  pressure  it  is 
erratic  ;  but  at  lower  pressures  it  again  becomes  more  constant, 
still  showing,  however,  a  tendency  to  increase  as  the  pressure  is 
decreased. 

"  3.  With  nitrogen  the  coefficient  of  expansion  is  lower  than 
the  normal  (^&?)  at  pressures  between  5  and  1  mm.  ;  at  lower 
pressures,  like  that  of  hydrogen,  its  coefficient  of  expansion 
decreases  ;  that  is,  the  gas  becomes  more  elastic. 

"  4.  So  far  as  it  was  possible  to  experiment  with  carbon 
dioxide,  its  behavior  appears  to  resemble  that  of  hydrogen  and 
nitrogen,  but  owing  to  the  tendency  which  it  has  to  condense 
and  cling  to  the  gauge,  trustworthy  measurements  were  im- 
possible to.  attain.  These  results  confirm  those  of  Mendeleeff1 
and  Siljestrom,2  although  they  are  deduced  from  thermal  ex- 
pansion, while  theirs  were  deduced  from  the  compressibility 
of  the  gas.  And  Bohr's  results3  as  regards  the  abnormality 
of  oxygen  were  also  confirmed,  although  likewise  by  a  different 
method." 

1  Annales  de  Chimie  et  de  Physique,  [5]  9,  111-116  (1876). 

2  Bihang  till  K.  Svenska   Vet.   Akad.  Handlingar.,  2,  1  (1873)  ;  Pog- 
gendorff's  Annalen,  151,  462-482,  573-603  (1874). 

3  Wiedei  luann's  Annalen,  27,  459-479  (1886). 


16 


EXPERIMENTAL  ESSAYS 

On  the  Constitution  of  Mixed  Gases;  On  the  Force  of  Steam 
or  Vapor  from  Water  and  other  liquids  in  different  tempera- 
tures, both  in  a  Torricellian  Vacuum  and  in  Air;  On  Evapora- 
tion; and  on  the  Expansion  of  Gases  by  Heat 

BY  JOHN  DALTOIT 

From  the  Memoirs  of  the  Literary  and  Philosophical  Society 

of  Manchester ,  volume  5,  part  2,  pages  595-602  (1802) 
Translated  into  German:  Gilbert's  Annalen,  volume  12, pages 
310-318  (1802) 


17 


CONTENTS. 

PAGE 

Object   .                     i -  .                         .            .  .  .19 

Necessity  of  drying  gases  experimented  with  .  .     19 

Apparatus  used;  manipulation           .            .  .  19,  20 

Results              .            .            .            .            .  20,  21 

Comparative  expansion  in  lower  and  upper  parts  of  thermo- 
meter scale         .            .            .            .  .  .21 

Experiments  with  gases  other  than  air            .  .  .21 

Conclusions      .            .            .            .            .  .  .21 

Biographical  Sketch     ...            .            .  .  .22 


18 


ON  THE  EXPANSION  OF  GASES  BY  HEAT. 

BY  JOHN  DALTON. 


THE  principal  occasion  of  this  essay  is  another  tm  the  same 
subject  by  Messrs,  de  Morveau  and  du  Vernois  in  the  first  vol- 
ume of  the  Annales  de  Chimie.  It  appearing  to  them  that  the 
results  of  the  experiments  of  De  Luc,  Col.  Hoi,  de  Saussure, 
Priestley,  Vandermonde,  Berthollet  and  Monge  did  not  suffi- 
ciently accord  with  one  another;  and  that  it  would  be  of 
importance  to  determine  not  only  the  whole  expansion  of  each 
gas  from  two  distant  points,  such  as  the  freezing  and  boiling, 
but  likewise  whether  that  expansion  be  uniform  in  every  part 
of  the  scale,  they  instituted  a  series  of  experiments  expressly 
for  those  purposes.  The  result  of  which  was  that  betwixt  the 
temperatures  of  32°  and  212°,  the  whole  expansion  of  one  gas 
differs  much  from  that  of  another,  it  being  in  one  case  about 
-^  of  the  original,  and  in  others  more  than  12  times  that  expan- 
sion; and  that  the  expansion  is  much  more  for  a  given  number 
of  degrees  in  the  higher  than  in  the  lower  part  of  the  scale. 
These  conclusions  were  so  extremely  discordant  with  and  even 
contradictory  to  those  of  others,  that  I  could  not  but  suspect 
some  great  fallacy  in  them,  and  found  it  in  reality  to  be  the 
fact:  I  have  no  doubt  it  arose  from  the  want  of  due  care  to 
keep  the  apparatus  and  materials  free  from  moisture. 

My  method  of  experimenting  on  this  subject  is  simple,  and 
therefore  less  liable  to  error.  A  straight  manometer  tube,  such 
as  has  been  mentioned,  is  duly  divided  into  equal  portions  of 
capacity;  it  is  then  dried  by  a  wire  and  thread,  and  the  open 
end  inserted  through  a  cork  into  a  phial  containing  sulphuric 
acid,  in  order  that  the  aqueous  vapour  may  be  drawn  out  of 
the  tube;  this  is  essential  if  we  operate  in  temperatures 
lower  than  that  of  the  atmosphere,  otherwise  not.  For  want 
of  this  attention,  Col.  Roi,  in  his  valuable  paper  in  the  Phil. 
Trans,  vol.  67,  has  been  led  into  some  erroneous  conclusions. 
—  A  small  column  of  dry  mercury  is  then  let  down  to  a  proper 

19 


MEMOIRS     ON 

point  in  the  manometer,  and  it  is  ready  for  experiment  with 
common  air. 

It  requires  some  address  to  fill  the  manometer  with  any  other 
gas. — I  succeeded  best  as  follows:  filled  the  tube  with  dry 
mercury;  then  pushed  down  a  wire  and  thread,  so  that  when 
the  wire  was  got  to  the  end  of  the  tube,  a  thick  covering  of 
thread  just  entered  the  open  end,  and  held  the  mercury  like  a 
cork,  so  that  ihe  tube  could  be  inverted  without  losing  the  con- 
tents; then  having  a  glass  funnel  with  a  perforated  cork  over 
the  water  apparatus,  containing  the  gas,  I  slipped  the  mano- 
meter through  the  hole  in  the  cork,  and  putting  my  hand  into 
the  water  under  the  funnel,  drew  the  wire  out  of  the  mano- 
meter, and  with  it  the  mercury;  upon  which  the  gas  entered 
the  manometer.  For  carbonic  acid  gas,  I  opened  the  sealed 
end  of  the  manometer,  drew  it  out  to  a  capillary  bore,  and 
forced  a  stream  of  the  gas  through  the  tube;  then  putting  my 
finger  on  the  other  end,  sealed  it  again  by  a  blowpipe,  and  let 
down  a  small  column  of  mercury  to  the  proper  point. 

When  the  manometer  was  to  be  exposed  to  a  heat  of  212°,  I 
used  a  Florence  flask  with  a  long  glass  tube  corked  into  it,  in 
such  sort  that  as  much  of  the  manometer  as  was  necessary  to 
be  exposed  to  the  temperature  might  be  in  the  tube;  then 
water  at  the  bottom  of  the  flask  was  made  to  boil  violently,  so 
that  a  constant  stream  of  vapour  issued  out  of  the  top  of  the 
glass  tube,  which  was  found  to  raise  the  thermometer  to  212°. 
Small  specks  of  white  paint  were  put  upon  the  divisions  of  the 
manometer  together  with  numbers  which  were  discernible 
through  the  containing  tube.  For  lower  temperatures  a  deep 
tin  vessel  containing  hot  water  was  used  in  which  the  mano- 
meter was  immersed,  the  water  being  well  agitated  previously 
to  each  observation. 

From  a  great  many  experiments  made  in  this  way  on  com- 
mon air,  and  likewise  upon  hydrogenous  gas,  oxygenous  and 
nitrous  gases,  and  carbonic  acid  gas,  I  can  assert  that  the  con- 
clusions of  DeLuc,  Roi,  Saussure,  Berthollet,  etc.,  are  nearly 
accurate  throughout,  and  that  those  of  de  Morveau  and  du  Ver- 
nois  are  extremely  inaccurate  in  the  higher  temperatures. 

I  have  repeatedly  found  that  1000  parts  of  common  air  of 
the  temperature  55°  and  common  pressure,  expand  to  1321 

20 


EXPANSION    OF    GASES 

parts  in  the  manometer;  to  which  adding  4  parts  for  the  cor- 
responding expansion  of  glass,  we  have  325  parts  increase  upon 
1000  from  55°  to  212°;  or  for  157°  of  the  thermometric  scale. 
As  for  the  expansion  in  the  intermediate  degrees,  which  Col. 
Roi's  experiments  show  to  be  a  slowly  diminishing  one  above 
the  temperature  of  57°,  but  which  de  Morveau's  on  the  con- 
trary show  to  be  a  rapidly  increasing  one  in  the  higher  part  of 
the  scale;  I  am  obliged  to  allow  that  Col.  Koi  is  right,  though 
it  makes  in  some  degree  against  an  hypothesis  I  have  formed 
relative  to  the  subject;  he  has  certainly  however  made  the 
diminution  too  great  from  72°  downwards,  owing  to  his  not 
perceiving  that  he  actually  destroyed  a  portion  of  the  elastic 
fluid  he  was  operating  upon  (aqueous  vapour)  in  reducing  its 
temperature  so  low;  if  his  air  had  been  previously  dried  by  sul- 
phuric acid,  etc.,  he  would  not  have  found  so  remarkable 
diminution  below  72  °.  My  experiments  give  for  77^°  above  55  °, 
167  parts;  for  the  next  77£°  only  158  parts:  and  the  expansion 
in  every  part  of  the  scale  seems  to  be  a  gradually  diminishing 
one  in  ascending. 

The  results  of  several  experiments  made  upon  hydrogenous 
gas,  oxygenous  gas,  carbonic  acid  gas  and  nitrous  gas,  which 
were  all  the  kinds  I  tried,  agreed  with  those  on  common  air 
not  only  in  total  expansion,  but  in  the  gradual  diminution  of 
it  in  ascending  :  the  small  differences  observed  never  exceeded 
6  or  8  parts  on  the  whole  325  ;  and  differences  to  this  amount 
will  take  place  in  common  air  when  not  freed  from  aqueous 
vapour  which  was  the  situation  of  all  my  factitious  gases. 

Upon  the  whole  therefore  I  see  no  sufficient  reason  why  we 
may  not  conclude,  that  all  elastic  fluids  under  the  samepressure 
expand  equally  by  heat — and  that  for  any  given  expansion  of 
mercury,  the  corresponding  expansion  of  air  is  proportionally 
something  less,  thehigher  the  temperature. 

This  remarkable  fact  that  all  elastic  fluids  expand  the  same 
quantity  in  the  same  circumstances,  plainly  shows  that  the  ex- 
pansion in  solid  and  liquid  bodies  seems  to  depend  upon  an  ad- 
justment of  the  two  opposite  forces  of  heat  and  chemical  af- 
finity, the  one  a  constant  force  in  the  same  temperature,  the 
other  a  variable  one,  according  to  the  nature  of  the  body  ; 
hence  the  unequal  expansion  of  such  bodies.  It  seems  there- 

21 


MEMOIKS    ON 

fore  that  general  laws  respecting  the  absolute  quantity  and  the 
nature  of  heat,  are  more  likely  to  be  derived  from  elastic  fluids 
than  from  other  substances.1 

Dalton,  in  his  New  System  of  Chemical  Philosophy  (London: 
1808),  page  19,  in  discussing  a  proposed  new  method  of  denot- 
ing temperature,  says  in  reference  to  the  expansion  of  gases: 
"The  volume  at  32°  is  taken  1000,  and  at  212°,  1376  accord- 
to  Gay-Lussac's  and  my  own  experiments.  As  for  the  expan- 
sion at  intermediate  degrees,  Gen.  Roy  makes  the  temperature 
at  midway  of  total  expansion,  116£  old  scale  ;  from  the  re- 
sults of  my  former  experiments  (Manch.  Mem.  Vol.  5,  Part  2, 
page  599),  the  temperature  may  be  estimated  at  119£;  but  I 
had  not  then  an  opportunity  of  having  air  at  32°.  By  my 
more  recent  experiments  I  am  convinced  that  dry  air  at  32  ° 
will  expand  the  same  quantity  from  that  to  117°  or  118°  of 
common  scale,  as  from  the  last  term  to  212°.  According  to 
the  theory  in  the  above  Table  it  appears,  that  air  of  117°  will 
be  1188,  or  have  acquired  one  half  its  total  expansion.  Now 
if  the  theory  accord  so  well  with  experiment  in  the  middle  of 
the  interval,  we  cannot  expect  it  to  do  otherwise  in  the  inter- 
mediate points.  " 

BIOGRAPHICAL  SKETCH. 

John  Dalton  was  born  in  Cumberland,  England,  in  the  year 
1766.  He  was  to  a  large  extent  self-taught  and,  when  grown, 
was  able  to  support  himself  by  teaching  school  while,  through 
the  kindness  of  a  friend,  who  helped  him  by  lending  him  books 
on  scientific  subjects,  he  studied  hard  to  acquire  a  knowledge 
of  natural  philosophy.  His  papers  on  meteorological  subjects 
drew  attention  to  him  and  in  1793  he  was  appointed  to  the  pro- 
fessorship of  mathematics  and  natural  philosophy  in  the  Man- 
chester New  College.  Simultaneous  observations  made  in  Cum- 

1  Note  by  Translator:  The  paper  concludes  with  an  exposition  of 
Dalton's  theory  that  the  absolute  temperature  increased  at  the  same  rate 
as  the  cube  root  of  the  volume  in  the  case  of  gases,  by  which  he  finds  the 
temperature  of  absolute  cold  to  be  1515°  below  0°  F. 

22 


EXPANSION    OF    GASES 

berland  and  at  Manchester  enabled  him  to  calculate  the  height 
of  the  aurora  from  the  earth's  surface.  The  fact  that  water 
vapor  exists  mixed,  and  not  combined,  in  the  air  was  announced 
by  him  at  this  time.  In  1794  he  called  attention  to  the  ex- 
istence of  color  blindness  or  "  Daltonism/'  as  it  was  sometimes 
called,  having  discovered  that  it  was  a  feature  of  his  own  vision. 
Continuing  his  meteorological  studies,  he  was  led  to  giving  a 
definition  of  the  "  dew-point/'  In  1800  he  noted  the  rise  of 
temperature  which  takes  place  in  gases  when  compressed.  Of 
the  four  important  papers  read  before  the  Manchester  Society 
in  1801,  the  fourth  is  the  one  quoted  in  full.  In  the  first  he 
brings  out  "  Dalton's  law  of  mixed  gases,"  assuming  that  gas 
particles  are  elastic  only  towards  particles  of  the  same  kind. 
In  the  second  paper,  "  On  the  force  of  steam/'  he  describes 
the  dew-point  hygrometer  and  predicts  the liquif action  of  gases 
by  cold  and  pressure.  In  the  third  paper  he  shows  that  evap- 
oration is  proportional  to  the  temperature,  whether  in  air  or  in 
vaouo.  That  four  such  contributions  to  science  should  have  been 
presented  at  one  time  is  striking  proof  of  the  extraordinary 
powers  of  their  author. 

The  data  upon  which  the  Law  of  Multiple  Proportions  is 
based  were  next  brought  forward  and,  soon  after,  in  1803-5,  the 
Atomic  Hypothesis  and  the  announcement  of  the  atomic 
weights  of  some  of  the  elements.  Following  the  promulgation 
of  his  views  in  Thomson's  System  of  Chemistry  (1807),  Dalton 
published  in  1808  his  New  System  of  Chemistry.  In  this  he  an- 
ticipated in  a  way  Dulong  and  Petit/s  Law,  for  he  seemed  to  as- 
sume for  the  atoms  of  all  elements  equal  capacity  for  heat. 

In  1825,  on  the  establishment  of  the  Royal  Society  Prize,  it 
was  first  bestowed  upon  Dalton  in  recognition  of  his  contribu- 
tions to  the  advancement  of  chemistry. 

Dalton  lived  until  1844,  but  his  classical  memoirs  practically 
all  belong  to  the  period  before  1815. 


KESEAECHES  UPON  THE  RATE  OF  EXPAN- 
SION OF  GASES  AND  VAPORS. 

BY    L.  J.   GrAY-LuSSAC. 

From  the  Annales  de  CMmie,  series  1,  volume  43,  pages  137 — 
175  (1802).  Translated  into  German,  Gilbert's  Annalen,  vol- 
ume 12,  pages  257—291  (1802). 


CONTENTS. 

PAGE 

Object  of  the  investigation      ....  .        .     27 

Effect  of  the  presence  of  moisture  upon  the  expansion  of 

29 


Earlier  investigations : 

Amontons  .        .        .        .        •        •  •        •         .30 

Nuguet       ,•                 .     '   .        •  .      •  •                 .31 
Lahire     =±v                •        •        •        •     -    •   .     •         -31 

Stancari      .        .        .        .       •.        .  .        .        .32 
Colonel  Roy        ... 

Saussure 33 

Priestley      ... 

Monge,  Berthollet  and  Vandermonde  .                  .34 

Guy  ton  de  Morvean  and  Duvernois   .  .35 

Charles       ....-,.  .        .     37 

Apparatus  and  manipulation : 

First  Method         .  .      .                         -  ...     38 

Same,  simplified  .         .  •  • 

Results  with  air    ...                 •  •     ^2 

Results  with  other  gases  .    43 

Method  employed  for  gases  soluble  in  water  . 

Results 45 

Experiments  upon  ether  vapor      .        .  .47 

Conclusions •  •                 .48 

Biographical  Sketch     .        . 


26 


RESEARCHES  UPON  THE  RATE  OF  EXPAN- 
SION OF  GASES  AND  VAPORS. 

BY  L.  J.  GAY-LUSSAC. 

PAKT   I. 
Object  of  this  Memoir. 

FOR  a  long  time  physicists  have  busied  themselves  with  [the 
problem  of]  the  expansion  of  gases;  but  their  researches  pre- 
sent such  great  discrepancies  in  the  results  that,  instead  of 
establishing  their  views,  they  call,  on  the  contrary,  for  a  more 
rigorous  investigation. 

The  expansion  of  vapors  has  attracted  the  attention  of  physi- 
cists to  a  less  extent.  Although  for  a  long  time  the  extraordi- 
nary properties  of  steam  have  been  recognized  and  the  most 
beneficent  applications  of  them  have  been  brought  about, 
Ziegler  and  Bettancourt  are  the  only  ones,  to  my  knowledge, 
who  have  endeavored  accurately  to  determine  them.  Their 
experiments  cannot  however  lead  to  a  knowledge  of  the  actual 
expansion  of  this  vapor;  since',  having  always  somo  water  in 
their  apparatus,  there  was,  for  each  new  degree  of  heat,  an 
expansion  of  the  vapor  produced  by  former  increments  of  heat 
and  an  increase  of  volume  due  to  the  formation  of  new  vapor — 
two  causes  which  combined  evidently  to  push  up  the  mercury 
in  their  manometer.1 


1  The  apparatus  of  Bettancourt  consists  of  a  boiler  of  copper  with 
a  cover  of  the  same  metal,  through  which  three  tubes  pass.  The  first 
serves  to  introduce  water  into  the  boiler;  through  the  second  is  inserted 
the  stem  of  a  thermometer  intended  to  show  the  temperature  of  the 
vapor,  and  to  the  third  is  attached  a  suitably  shaped  barometer  tube  to 
measure  the  tension  of  this  same  vapor.  A  vacuum  is  produced  in  the 
boiler  with  the  aid  of  a  pneumatic  pump,  which  is  connected  by  means 
of  a  tube  provided  with  a  stop  cock.  The  apparatus  of  Ziegler  differs 
but  little  from  that  of  Bettancourt;  but  Ziegler  not  having  produced,  as 
Bettancourt  did,  a  vacuum  in  his  boiler,  there  results  a  great  difference 
in  their  experimental  data.  (Architecture  hydraulique  de  Prony,  Tome 
II). 

27 


MEMOIRS    ON 

The  thermometer,  as  it  exists  to-day,  cannot  serve  to  show 
with  accuracy  relative  amounts  of  heat,  because  we  do  not  yet 
know  what  relation  exists  between  the  degrees  of  the  ther- 
mometer and  the  quantities  of  heat  which  they  can  indicate. 
We  believe,  it  is  true,  in  general,  equal  divisions  of  its  scale 
correspond  to  equal  increments  of  caloric;  but  this  view  is 
supported  by  no  very  positive  fact. 

It  must  therefore  be  admitted  that  we  are  far  from  having 
exact  knowledge  of  the  expansion  of  gases  and  vapors  and  of 
the  movements  of  the  thermometer;  and  in  the  meantime 
there  is  every  day  a  call,  in  physics  and  in  chemistry,  to  reduce 
a  given  volume  of  gas  at  one  temperature  to  another;  to  meas- 
ure the  heat  given  off  or  absorbed  in  the  change  of  constitution 
of  substances,  that  given  off  or  absorbed  by  the  same  body  in 
passing  from  one  temperature  to  another;  in  the  arts,  in  calcu- 
lating the  efficiency  of  steam  engines,  in  ascertaining  the  rate 
of  expansion  of  many  substances;  in  meteorology,  in  deter- 
mining the  quantity  of  water  held  in  solution  in  the  air — a 
quantity  which  varies  with  its  temperature  and  its  density  and 
follows  a  law  as  yet  unknown.  Finally,  in  the  preparation  of 
tables  of  refraction  by  astronomers  and  in  the  application  of  the 
barometer  to  the  measurement  of  altitudes,  it  becomes  indis- 
pensable to  know  with  accuracy  the  temperature  of  the  air  and 
the  law  of  its  expansion. 

Although  these  facts  have  made  it  very  desirable  to  engage 
in  a  work  of  such  general  application,  the  difficulty  of  the 
investigations  which  it  demands  would  have  prevented  my  de- 
voting myself  to  it,  had  I  not  been  on  the  other  hand  strongly 
urged  by  Citizen  Berthollet,  whose  pupil  I  have  the  honor  to  be. 
To  him  I  owe  the  means  necessary  for  the  prosecution  of  this 
research,  during  which  I  have  often  been  assisted  by  his  advice 
and  by  that  of  Citizen  Laplace:  men  whose  reputation  will  add 
to  the  confidence  my  work  would  inspire. 

The  researches  I  have  undertaken  upon  the  law  of  the  ex- 
pansion of  gases  and  vapors,  and  upon  the  movements  of  the 
thermometer,  not  being  yet  complete,  I  have  for  my  object  in 
this  memoir  only  to  investigate  the  expansion  of  gases  and 
vapors  for  one  definite  rise  of  temperature  and  to  make  it  clear 
that  this  is  the  same  for  all  these  fluids;  but  before  giving  an 

28 


EXPANSION    OF    GASES 

account  of  my  experiments,  I  think  I  ought  to  give  an  histori- 
cal survey  of  what  has  been  done  upon  this  subject.  And  as 
I  add  at  the  same  time  some  comments  upon  the  means  which 
have  been  employed,  I  intend  to  preface  them  with  a  discus- 
sion of  one  of  the  chief  causes  for  uncertainty  which  can 
enter  into  this  class  of  investigations.  Although  it  is  very 
important  and  although  it  seems  to  have  been  unknown  to 
the  majority  of  the  physicists  who  have  studied  the  expansion 
of  gases,  it  will  be  enough  for  me  merely  to  state  it  to  make 
its  influence  felt.  What  I  say  of  atmospheric  air  will  apply  to 
other  gases. 

This  cause  of  uncertainty  is  due  to  the  presence  of  water  in 
the  apparatus.  As  a  matter  of  fact  if  a  few  drops  of  this  fluid 
are  left  in  a  vessel  filled  with  air  whose  temperature  is  then 
raised  to  that  of  boiling  water,  this  water,  on  passing  into  the 
form  of  a  vapor,  will  occupy  about  1800  times  as  great  a  volume 
as  at  first,  and  by  this  means  will  drive  out  a  very  large  part  of 
the  air  originally  enclosed  in  the  vessel.  It  necessarily  follows 
that  when  this  vapor  is  condensed — and  therefore  occupies  a 
space  1800  times  as  small — we  should  ascribe  to  the  air  remain- 
ing in  the  vessel  an  expansion  far  too  great;  for  it  would  be 
assumed  that  it  was  this  air  which  at  the  temperature  of  boiling 
water  filled  all  the  space  in  the  vessel.  If  we  do  not  carry  the 
temperature  up  to  this  point,  the  same  source  of  inaccuracy 
will  nevertheless  exist,  and  its  extent  will  be  proportional  to 
the  temperature  at  which  we  stop:  for  in  this  case  the  water 
will  not  all  evaporate,  but  the  air  will  dissolve  more  and  more  as 
the  temperature  rises  and  will  consequently  assume  a  greater  and 
greater  volume  over  and  above  that  which  it  owes  to  the  heat; 
so  that  when  we  pass  to  a  lower  temperature  the  volume  of  air  /  v 
which  fills  all  the  space  in  the  vessel  will  decrease  from  two 
causes:  (1)  through  the  .loss  of  its  caloric,  (2)  through  that  of 
the  water  which  it  holds  in  solution.  Too  great  an  expansion 
would  thus  be  assumed  for  the  air. 

Speaking  generally,  whenever  there  is  enclosed  with  gases 
any  liquid,  or  even  any  solid  which  like  sal  ammoniac,  for 
example,  can  be  dissolved  or  become  vaporized  at  the  tempera- 
ture to  which  it  is  to  be  raised,  errors  must  of  necessity  result 
in  the  determination  of  the  expansion  of  these  gases. 

29 


MEMOIRS    OX 

PART  II. 

Historical  Sketch  of  what  has  been  done  upon  the 
Expansion  of  Gases. 

The  expansion  of  atmospheric  air  by  heat  was  well  known 
before  the  time  of  Amontons,  but  this  physicist  is  apparently 
the  first  to  seek  to  determine  its  amount  for  a  given  rise  of 
temperature.  To  attain  this  result  he  enclosed  some  air  with 
the  aid  of  mercury  in  a  flask  connected  with  one  of  the  arms 
of  a  reversed  siphon,  and  placed  this  apparatus  in  a  bath  of  hot 
water.1  The  air  expanded  by  the  heat  presses  upon  the  mer- 
cury and  forces  it  into  the  other  branch  of  the  siphon;  so  that 
he  judged,  by  the  height  of  the  mercury  compared  with  its 
level  in  the  flask,  the  tension  the  air  had  reached. 

From  various  experiments  made  upon  different  volumes  of 
air,  he  concludes  (Mem.  de  I'acad.,  1699,  1702):  (1)  "That  the 
heat  of  boiling  water  has  limits  which  it  does  not  pass;  (2) 
that  various  volumes  of  air  increase  their  tensions  at  the  same 
rate  for  equal  degrees  of  heat,  and  vice  versa;  (3)  that  the  heat 
of  boiling  water  increases  the  tension  only  until  it  is  capable 
of  sustaining  about  the  weight  of  a  column  of  mercury  of  ten 
inches'  height/' 

It  appears  then  that,  however  compressed  a  volume  of  air 
may  be,  the  heat  of  boiling  water  always  increases  its  tension 
one  third;  that  is  to  say,  a  volume  of  air  compressed,  for 
example,  under  a  column  of  60  inches  of  mercury,  including 
the  weight  of  the  atmosphere,  will  support,  at  the  temperature 
of  boiling  water,  a  column  of  mercury  of  about  80  inches.  He 
therefore  concludes  "that  the  same  degree  of  heat,  small  as  it 
may  be,  will  always  increase  the  tension  of  the  air  more  and 
more  as  this  air  is  supporting  a  greater  and  greater  weight/' 

If  Amontons  had  started  from  a  degree  of  heat  more  clearly 
defined  than  what  he  calls  an  average, — which  would  have  been 
at  that  time  scarcely  possible — it  would  have  been  possible  to 
calculate  from  his  experiments  with  sufficient  approximation 

1The  air  enclosed  in  the  flask,  not  being  able  to  escape  when  the 
mercury  is  poured  in,  is  a  little  more  compressed  than  it  would  be 
naturally;  but  if  no  other  pressure  than  that  of  the  atmosphere  is  de- 
sired, it  would  be  very  easy  to  avoid  this  slight  inconvenience. 

30 


EXPANSION    OF    GASES 

the  expansion  of  atmospheric  air;  yet,  since  he  conducted  his 
comparisons  with  volumes  of  gas  of  very  unequal  density,  one 
may  conclude  from  them  that,  however  dense  a  volume  of  air 
may  be,  the  increase  of  elasticity  which  this  air  acquires  for  the 
same  degree  of  heat  always  bears  the  same  relation  to  that  which 
it  had  prior  to  the  experiment. 

Nuguet,  in  seeking  to  verify  the  results  of  Amontons,  ob- 
tained others  entirely  unlike  them.  In  one  of  his  experiments, 
the  volume  of  the  air  expanded  by  the  heat  of  boiling  water 
and  the  original  volume  were  to  one  another  as  2  to  1,  and  in 
two  other  experiments  as  16  to  1.  His  apparatus  consisted  of  a 
flask  inverted  and  sunk  in  a  water  bath  whose  temperature  he 
raised  to  that  of  boiling  water.  It  is  evident  that  this  appara- 
tus was  extremely  defective,  since  the  air  in  it  was  always  in 
contact  with  water;  and  Nuguet  had  in  addition  let  some 
water  into  his  flask.  It  is  not  surprising,  therefore,  that  he 
obtianed  results  so  discordant  and,  so  to  speak,  so  extraordin- 
ary. (Mem.  de  I'acad.,  1708.  Lahire.) 

This  great  difference  between  the  results  of  Amontons  and 
those  of  Nuguet  upon  the  rate  of  expansion  of  atmospheric 
air,  and  the  realization  that  it  had  been  subjected  to  experi- 
ment under  conditions  which  were  not  usual,  led  Lahire  to  ap- 
ply himself  to  the  same  problem.  The  apparatus  of  which  he 
made  use  was  identical  with  that  of  Amontons,  except  that  the 
bulb  carried  a  small  tube  which  he  sealed  after  having  intro- 
duced the  mercury.  By  this  means,  the  mercury  being  at  the 
same  level  in  the  bulb  and  in  the  syphon,  the  air  which  he  sub- 
jected to  experiment  was  no  more  compressed  than  the  sur- 
rounding air.  With  this  apparatus  Lahire  found,  first,  in  one 
experiment  that  the  air  expanded  from  an  average  temperature 
up  to  that  of  boiling  water,  could  not  sustain  a  column  of  mer- 
cury of  one  third  of  the  weight  of  the  atmosphere;  later,  he 
found  in  another,  the  thermometer  being  lower  and  the  barom- 
eter higher  than  in  the  former  experiment,  that  the  air,  ex- 
panded by  the  heat  of  boiling  water,  could  not  support  a  col- 
umn of  mercury  so  high  as  the  former  one.  These  two  results 
are  evidently  contradictory;  but  Lahire  suspected  no  error  and 
drew  the  conclusion  from  them  that  we  are  bound  to  admit 
that  we  do  not  yet  know  the  nature  of  the  air. 

31 


MEMOIRS    ON 

In  order  to  explain  the  great  difference  which  existed  be- 
tween his  results  and  those  of  Nuguet,  a  difference  far  too 
great  not  to  be  due  to  some  outside  influence,  Lahire  noticed 
that  Nuguet  had  let  a  little  water  into  his  apparatus;  and  from 
this  fact  he  concluded  that  it  might  be  this  water  which,  on  be- 
ing converted  into  vapor  and  expelling  a  large  part  of  the  air 
enclosed  in  the  flask,  had  produced  so  great  an  expansion.  He 
was  thoroughly  confirmed  in  his  opinion  by  the  result  of  an  ex- 
periment carried  out  after  Nuguet's  method,  in  which  he  let  a 
little  water  into  the  flask;  for  he  found  that  the  volume  of  the 
air  expanded  from  the  average  temperature  up  to  that  of  boil- 
ing water,  and  the  original  volumes  were  to  one  another  as  35£ 
is  to  1.  (Mem.  de  I'acad.,  1708.) 

At  the  same  time  M.  Stancari  of  Bologna  showed  that  water 
increases  to  a  considerable  degree  the  volume  of  air  at  a  tem- 
perature but  slightly  raised.  We  therefore  owe  to  these  two 
physicists  the  important  discovery  of  the  influence  of  water  up- 
on the  expansion  of  atmospheric  air;  yet  although  they  have 
by  their  experiments  given  the  matter  prominence,  it  has  since 
been  generally  overlooked.  To  the  slight  attention  paid  to 
this  influence  must  be  ascribed  the  great  divergencies  found  in 
the  results  of  physicists  upon  the  expansibility  of  gases. 

It  is  known  that  the  altitudes  to  which  one  ascends  in  the 
atmosphere  are  given  by  the  logarithms  of  the  corresponding 
heights  of  the  barometric  column.  If  the  density  of  the  air  were 
always  the  same,  it  would  be  easy  thus  to  calculate  the  alti- 
tude of  one  place  above  another  stated  place,  by  observing  the 
barometer  there.  It  would  therefore  be  important  to  distin- 
guish the  causes  that  affect  the  density  of  the  air,  in  order  to 
make  the  necessary  corrections  in  the  heights  given  by  the  ba- 
rometer. 

Deluc,  who  has  inaugurated  a  new  era  in  this  department  of 
physics,  recognized  in  heat  one  of  these  causes.  In  order 
clearly  to  identify  its  effect,  he  began  by  endeavoring  to  fix  the 
temperature  at  which  the  logarithms  indicate  directly  the  cor- 
rect altitudes,  and  found,  on  comparing  numerous  observations 
made  at  places  whose  altitudes  he  had  determined  with  accur- 
acy, that  this  was  the  case  at  the  temperature  of  16f  °  of  the 
thermometer  graduated  in  80  divisions,  and  this  he  calls  tem- 

32 


EXPANSION    OF    GASES 

perature fixe.  Therefore  to  make  correction  for  the  effects  of 
heat  above  and  below  this  fixed  point,  he  again  compared  the 
altitudes  found  from  the  logarithms  with  those  he  had  meas- 
ured, attributing  to  heat  the  variations  of  the  first  from  the 
second,  and  drew  the  conclusion  that  "in  the  neighborhood  of 
the  fixed  temperature,  the  correction  for  one  degree  of  the 
thermometer  would  be  to  the  altitude  of  the  place  as  1  is  to 
215."  (Recher,  sur  Us  modif.  de  Vat.,  IV  Part,  Ch.  III.) 

Colonel  Roy  has  found  a  far  greater  rate  of  expansion  for 
air.  According  to  him,  in  the  neighborhood  of  15°  on  a  ther- 
mometer graduated  in  80  divisions,  air  expands  T^  of  its  vol- 
ume for  each  degree.  He  also  found  that  moist  air  expands 
much  more  than  dry  air;  but  Saussure  noted  that  in  carrying 
out  his  experiments,  Col.  Roy  had  admitted  into  his  manome- 
ter either  water  in  a  liquid  state  or  water  vapor  and  had  con- 
fused two  things  which  should  be  distinguished,  namely,  the 
conversion  of  water  into  an  elastic  fluid,  and  the  expansibility 
of  air  mixed  with  this  vapor.  (Philos.  transact.,  1777,  p.  704.) 

Saussure  determined  the  rate  of  expansion  of  air  in  the  neigh- 
borhood of  6°  to  be  yfa  of  its  volume  for  each  degree.  His  ex- 
periments were  performed  with  a  large  flask  in  which  were 
enclosed  a  thermometer  and  a  barometer  to  indicate  the  varia- 
tions of  the  temperature  of  the  air  and  the  corresponding  ten- 
sion acquired.  In  order  to  study  the  effect  of  water  upon  the 
expansion  of  air,  he  enclosed  in  his  flask  air  of  varying  degrees 
of  dryness,  avoiding  the  formation  anew  of  vapor,  and,  far  from 
finding  this  air  more  expansive  than  very  dry  air,  he  thought  he 
had  discovered,  on  the  contrary,  that  very  dry  air  was  even  a 
little  more  expansive  than  air  which  was  very  moist,  but  was 
holding  its  moisture  all  the  time  entirely  uncondensed.  (Es- 
sai  sur  I'hygrometrie,  page  1 08.) 

Up  to  this  time  physicists  had  limited  themselves  to  the  ex- 
pansion of  atmospheric  air,  and  the  first  to  occupy  himself  with 
that  of  other  gases  is  the  celebrated  Priestley.  He  proceeded 
as  follows  : 

After  having  filled  a  flask,  over  mercury,  with  the  gas  he 
wished  to  test,  he  fitted  to  it  a  bent  tube,  one  of  whose  arms  was 
nearly  horizontal,  and  left  a  little  mercury  in  the  neck  of  the 
flask  so  that  the  expansion  of  the  gas  could  push  it  into  the 

33 


MEMOIRS    ON 

tube.  This  done,  he  put  his  apparatus  in  a  small  wooden  box, 
introduced  a  thermometer,  and  carried  it  into  rooms  at  differ- 
ent temperatures  :  the  expanded  air  caused  the  mercury  to 
move  a  greater  or  less  distance  along  the  tube,  and  it  was  by 
this  distance  measured  in  inches  that  Priestley  determined  the 
expansibility  of  different  gases.  As  all  the  experiments  were 
made  with  the  same  flask  and  the  same  tube,  which  he  probably 
inclined  always  in  the  same  way,  they  give  a  ratio  among  the 
expansibilities  of  different  gases,  but  not  the  actual  expansion ; 
for  it  would  be  necessary  to  know  for  that  purpose  the  volume 
of  that  part  of  the  tube  traversed  by  the  mercury  in  compari- 
son with  that  of  the  flask,  and  to  know,  in  addition,  the  exact 
inclination  of  the  tube,  of  which  Priestley  makes  no  mention. 
I  shall  not  pause  longer  to  discuss  these  experiments  ;  all  the 
more  as  Priestley  himself  did  not  put  much  confidence  in  them 
and  wished  to  repeat  them  under  better  conditions.  Assuming 
the  volumes  of  the  different  gases  equal,  the  expansion  measured 
in  inches  along  the  tube,  for  4.44°  of  the  thermometer  gradu- 
ated in  80  divisions, 1  would  be  : 

Ordinary  air        .        .        .        .        .   1.32  inches 
Hydrogen  gas      .        .        .        .        .  2.05      " 
Nitrous  gas         ...        .        .  2.02      " 
Carbonic  acid  gas       .        .        .        .   2.20      " 
Muriatic  acid  gas     •  ...        .        .   1.33 
Oxygen  gas      '    .'  .        .        .   2.21 

Nitrogen  gas 1.65 

Sulphurous  acid  gas  ....   2.37 

Fluoric  acid  gas 2.83 

Ammoniacal  gas .       ..        .-       .        .  4.75 

(Experiments  and  Observations,  etc.,  Boole  VII,  Section  VI.) 
In  a  memoir  printed  among  those  of  the  Academy  for  the 
year  1786,  Citizens  Monge,  Berthollet  and  Vandermonde  have 
concluded  from  an  experiment  that,  for  one  degree  atmospheric 
air  expands  TW.^s  °f  ^s  volume,  and  hydrogen  gas  rffi.ff*- 

Lastly,  Citizen  Guyton,  realizing  how  little  accord  there  was 
on  [the  subject  of]  the  rate  of  expansion  of  atmospheric  air, 

1  Note  by  Translator:  On  an  80-degree  thermometer  scale  (e.  g. 
Reaumur's)  4.44°  is  the  equivalent  to  10°  Fahrenheit.  The  latter  was 
evidently  the  temperature  interval  employed  by  Priestley. 

34 


EXPANSION    OF    GASES 

and  that  there  were  still  no  direct  experiments  on  record  which 
determined  the  expansion  of  gases  for  slightly  elevated  degrees 
of  heat  and  for  successive  degrees  near  together,  undertook, 
with  Citizen  Duveriiois,  to  throw  some  light  upon  this  matter. 
As  their  work  is  the  most  recent,  I  shall  pause  a  moment  to 
endeavor  to  show  what  the  causes  are  which  were  able  to  affect 
their  result. 

Their  apparatus  consisted  of  a  flask  fitted  with  a  bent  tube 
by  means  of  which  the  air  expelled  from  the  flask  by  heat  was 
caught  in  a  receiver  in  the  mercury  trough.  The  flask,  full  of 
the  gas  they  wished  to  subject  to  experiment,  was  immersed  in 
a  bath  at  the  temperature  of  melting  ice  and  was  held  there 
by  an  iron  cover.  They  heated  the  bath  to  20°,  40°,  60%  80°, 
successively,  and  caught  in  different  receivers  the  gas  forced 
out  by  expansion  through  each  of  these  intervals;  they  finally 
determined  the  volumes  of  air  escaping  from  the  flask  by 
measuring  them  in  their  respective  receivers  after  having 
reduced  them  to  the  temperature  of  melting  ice,  and  thus 
found  the  volume  of  that  remaining  in  the  flask.1  But  apart 
from  the  fact  that  their  apparatus  made  it  necessary  for  them 
to  determine  many  constants — which  must  interfere  with  the 
accuracy  of  their  results — I  note  that,  after  the  sinking  of  the 
bent  tube  in  the  mercury,  not  having  introduced  some  more 
air  into  the  flask  to  replace  the  mercury  which  was  pushed  into 
the  tube  as  a  result  of  the  pressure  of  the  mercury  of  the  bath, 
several  degrees  of  heat  would  be  needed  before  a  single  bubble 
of  air  escaped  from  the  flask;  so  that,  if  they  had  made  use  of 
lesser  intervals,  as,  [for  example]  of  5°  each,  they  would  have 
found  that,  starting  from  zero,  the  first  degrees  of  heat  would 
have  shown  no  expansion  in  the  different  gases.  Indeed  they 
have  observed  an  expansion  for  the  first  20  degrees  which,  for 
the  majority  of  the  gases,  is  far  too  small. 

This  source  of  error,  although  serious,  would  not  have  car- 
ried the  results  of  Citizens  Guyton  and  Duvernois  so  wide  of 
the  truth,  had  there  not  been  others  still  more  serious.  Thus 
I  suspect  that  their  flask  had  not  been  properly  dried  and  that 
a  little  water  may  have  got  in  during  the  introduction  of  the 


1  Annales  de  Chimie,  Vol.  I. 

35 


MEMOIRS     ON 

gases.  Had  a  decigram  of  water  remained,  it  would  have 
served  to  aUect  their  results  iu  a  marked  way,  especially  towards 
the  higher  degrees,  where,  in  changing  into  an  elastic  fluid,  it 
would  have  forced  a  large  part  of  the  air  out  of  the  flask. 

In  this  way  can  be  explained  the  noticeably  increasing  pro- 
gression which  they  have  determined  for  all  the  gases,  whereas 
they  ought  to  have  found  a  decreasing  one,  on  lowering  to  the 
temperature  of  melting  ice  the  amount  forced  out  by  each 
expansion.  I  note  in  connection  with  this  point,  that  Citizen 
Guy  ton  expresses  himself  as  regards  the  expansion  of  hydrogen 
gas  as  follows:1  "  The  four  [volumes]  resulting  from  the  expan- 
sion were  caught  this  time  in  a  receiver  which  had  been  sur- 
rounded with  vessels  filled  with  ice.  In  spite  of  this,  the 
mercury  of  the  little  trough  showed  upon  the  thermometer  [a 
temperature]  2,  3,  4,  6  degrees  above  zero,  while  the  water  of 
the  bath  was  at  the  same  moment  at  20,  40,  60,  and  80  degrees 
— a  thing  which  could  produce  some  inaccuracy  in  the  deter- 
mination of  each  of  these  quantities,  but  which  cannot  be  of 
much  consequence,  the  expansion  being  very  slight  through 
these  first  degrees." 

From  this  one  may  conclude  that  these  physicists  gave  no 
more  care  to  reducing  the  volumes  of  the  other  gases  to  zero; 
and,  if  this  be  the  case,  there  results  another  source  of  uncer- 
tain tyQin  their  experiments. 

In  comparing  the  volumes  of  gas  left  in  the  flask  with  those 
that  had  been  driven  out  by  heat,  Citizens  Guyton  and  Duver- 
nois  have  found  that  the  gases  oxygen,  hydrogen,  carbonic  acid 
and  atmospheric  air  had  shown  a  contraction  and  have  given 
as  its  cause  combinations  which  had  taken  place  during  the 
time  of  the  experiments.  Employing  mercury  which  was  very 
pure  and  free  from  oxide,  I  have  been  unable  to  detect  any 
noticeable  action  between  the  metal  and  these  gases  from  the 
temperature  of  melting  ice  up  to  that  of  boiling  water. 

Below  is  a  table  of  the  results  of  Citizens  Guyton  and 
Duvernois  ;  they  have  enclosed  between  parentheses  those  in 
which  they  have  little  confidence. 

lAnnales  de  Chimie,  T.  I,  page  284. 

36 


Wtw  wvisrow 


EXPANSION     OF     GASES 


From  0 

to  20° 


From  20 
to  40° 


From  40  °  I  From  60  °  I  From  0 

to  60°  to  80°          to  80° 


Ordinary  air 
expands 

Vital  air 
Nitrogen  gas 
Hydrogen  gas 

Nitrous  gas 

Carbonic 

acid  gas 

Ammoniacal 

gas 


[s.fcy)         T.itaT 


'r.W    |  (3  +  y.W) 


T.V* 


Mn) 


.W 


.V 


s.r 


T.W 


Before  going  further,  I  ought  to  say  that,  although  I  had 
noted  a  great  many  times  that  the  gases  oxygen,  nitrogen, 
hydrogen,  carbonic  acid  and  atmospheric  air  expand  to  the 
same  extent  from  0°  to  80°,  Citizen  Charles  had,  fifteen  years 
before,  discovered  the  same  property  in  those  gases  ;  but,  never 
having  published  his  results,  it  was  by  the  greatest  chance  that 
I  learned  of  them.  He  had  also  endeavored  to  determine  the 
rate  of  expansion  of  gases  soluble  in  water  and  had  found  for 
each  a  characteristic  rate  of  expansion  different  from  that  of 
the  other  gases.  In  respect  to  this  my  conclusions  differ  much 
from  his. 

Citizen  Charles  employed  as  his  apparatus  a  barometer  the 
chamber  of  which  was  of  a  large  size.  The  gas  which  he  wished 
to  submit  to  experiment  was  enclosed  in  the  reservoir  of  the 
barometer  at  the  temperature  0°  and  under  a  pressure  of  28 
inches  of  mercury.  When  this  barometer  was  submerged  in 
boiling  water,  the  mercury  rose  in  the  tube  and  the  excess  of 
the  entire  column  over  that  of  28  inches  indicates  the  tension 
the  gas  had  acquired  ;  but  Citizen  Charles  having  been  kind 
enough  to  show  me  the  apparatus,  I  saw  that  the  tube  of  the 
barometer  was  very  large  in  proportion  to  the  capacity  of  the 
reservoir  ;  so  that  the  rise  of  the  mercury  above  28  inches  did 
not  show  all  the  tension  the  gas  had  acquired,  since  for  that  it 
would  be  necessary  that  its  volume  in  the  reservoir  had 
remained  constant.  It  therefore  seems  to  me  that  the  true 

37 


MEMOIRS     ON 

rate  of  expansion  of  gases  cannot  be  deduced   from  these  ex- 
periments. 

PAKT  III. 

Description  of  Apparatus. 

A  flask  B  (Fig.  1)  is  provided  with  an  iron  tap  to  which  a 
bent  tube  ID  (See  Fig.  2)  can  be  fitted.  The  key  of  the  tap 
carries  a  lever  LL  pierced  at  its  two  ends  to  receive  two  cords 
by  which  one  can  open  and  close  the  tap  under  water. 


FIG.  1 


To  introduce  gases  into  the  flask,  I  made  use  of  a  glass  bell 
jar  M  (Fig.  1),  to  which  are  fitted  a  tap  and  a  bent  tube  T, 
and  sunk  in  a  vessel  QS.  On  pouring  water  into  the  vessel 
and  opening  the  tap,  the  gas  compressed  in  the  bell  jar  escaped 
by  the  tube  and  filled  the  flask  B  placed  mouth-downward  in 
the  mercury  bath  PO.  When  the  flask  is  full,  I  close  the  tap, 
adjust  the  tube  ID  (Fig.  2)  and  fix  it  in  a  cylindrical  iron  cage 
EFGH,  which  I  then  place  in  a  copper  vessel  AD,  full  of 
water.  In  order  that  there  might  be  no  communication  between 
the  outside  air  and  the  gas  enclosed  in  the  flask  when  the  tap 
is  opened,  I  lowered  the  end  of  the  tube  ID  one  or  two 
millimeters  into  the  small  mercury  bath  KX.  This  done,  I 
heat  the  bath  and  at  intervals  of  10°,  let  us  say,  open  the  tap 
and  immediately  close  it  again.  The  gas,  tending  to  expand 

38 


EXPANSION    OF    GASES 


on  account  of  the  heat,  escapes  rapidly  from  the  flask  and  has 
soon  driven  out  the  atmospheric  air  which  filled  the  tube  ; 
from  40°  on  the  tap  can  with  safety  be  left  open  until  the  end 
of  the  operation  :  I  prefer  however  alternately  to  open  it  and 
close  it,  as  I  find  that  [under  these  circumstances]  the  gas  in 
the  flask  comes  more  rapidly  to  the  temperature  of  the  bath. 
After  15  or  20  minutes  of  boiling — a  sufficient  time  for  every- 


HORIZONTAL  SECTION 
ON  YZ 


A\ 


FIG.  2. 


thing  to  come  to  the  same  temperature — I  remove  the  end  of 
the  tube  ID  from  the  mercury,  in  order  to  secure  equilibrium 
between  the  outside  air  and  the  gas  in  the  flask,  and  then  close 
the  tap.  After  having  cooled  the  bath  with  ice  or  water,  I 
remove  the  apparatus,  disconnect  the  flask  from  which  I 
remove  the  tube  ID  and  also  the  lever  LL  and  submerge  it 
completely  in  a  bath  of  known  temperature  where  I  leave  it 
long  enough  for  it  to  come  perfectly  to  that  temperature. 

Now,  on  opening  the  tap,  there  enters  the  flask  a  volume  of 
water  which  is  exactly  equal,  when  equilibrium  is  restored,  to 
that  of  the  gas  which  has  been  driven  out  by  the  heat.  The  tap 

39 


MEMOIRS     ON 


being  closed,  I  remove  the  flask,  carefully  dry  its  surface  and 
weigh  it  in  this  condition  ;  afterwards  I  weigh  it  full  of  water 
and  empty,  recording  the  results  of  each  weighing.  These 
being  known,  I  find  the  volume  of  the  flask  by  subtracting  the 
weight  of  the  empty  flask  from  that  of  the  flask  filled  with 
water,  and  the  volume  of  the  water  which  represents  the  volume 
of  air  driven  out  of  the  flask  by  the  heat,  by  subtracting,  again, 
the  weight  of  the  empty  flask  from  that  of  the  flask  when  it 
contained  this  water.  It  will  thus  be  very  easy  to  determine 
the  relationship  between  the  original  volume  and  the  volume 
when  expanded. 

This  method  has  the  advantage  of  possessing  great  accuracy; 

for,   as  the   volumes  are   found   from  the   weights,  the  error 

which  can  be  made  in  this  determination  must  be  very  small, 

even  when  use  is  made  of  balances  of  no  great  sensibility. 

The  apparatus  I  have  described  is  simple  enough   in  itself, 

yet,  as  it  calls  for  the  use  of  ce- 
ments and  of  a  tap  which  must 
be  of  iron  by  reason  of  the  mer- 
cury, its  manipulation  is  some- 
what difficult.  It  will  not  there- 
fore be  out  of  place  to  describe 
another  apparatus  also  which  I 
have  used  and  which,  along  with 
great  simplicity  and  easy  manipu- 
lation, possesses  at  least  nearly 
advantages  of  the  former  one. 
It  is  a  simple  flask  D  (Fig.  I,  Plate  II) 
[See  Fig.  3]  whose  neck  must  be  at  least 
a  decimeter  long.  After  having  filled  it 
with  the  gas  I  wish  to  subject  to  experi- 
ment, in  the  way  already  described,  I  in- 
troduce its  neck  about  two  centimeters 
into  the  mercury  contained  in  an  ordinary 
vessel  OM,  and  fasten  it  in  an  iron  frame 
as  in  the  case  of  the  former  apparatus. 
If  I  immerse  it  in  this  condition  in  a  bath  of  hot  water,  the  gas 
expanded  by  the  heat,  in  order  to  escape,  will  have  to  overcome, 
not  only  the  pressure  of  the  mercury  in  the  vessel,  but  that  of 

40 


EXPANSION    OF    GASES 

the  water  of  the  bath  as  well.  To  do  away  with  this  incon- 
venience, I  introduce  into  the  neck  of  the  flask  the  end  of  a 
very  narrow  bent  tube  B,  taking  care  to  keep  the  end  G  closed 
until  it  has  been  lowered  into  some  mercury.  To  support  the 
tube,  I  fasten  to  the  middle  of  it  a  cord  on  the  end  of  which  I 
hang  a  weight  and  pass  it  over  a  support,  in.  such  a  way  that 
the  weight  by  its  action  tends  to  lift  the  tube.  The  apparatus 
being  thus  arranged,  I  place  it  in  a  glass  tank  where  there  is  a 
depth  of  water  equal  to  that  which  should  be  in  the  bath,  I 
open  for  a  moment  the  end  of  the  tube  in  order  to  establish 
equilibrium  with  the  pressure  of  the  outside  air,  and  close  it 
again  at  once.  As  there  is  a  scale  whose  divisions  are  very 
small  upon  the  neck  of  the  flask,  I  read  the  exact  level  of  the 
mercury  ac  inside  the  neck  of  the  flask  and  record  it,  since  it 
is  to  this  level  that  the  volume  of  the  flask  extends.  The  end 
of  the  tube  B  must  be  raised  above  the  level  ac,  for  otherwise 
the  mercury  will  enter  the  tube  and  offer  a  resistance  to  the 
escape  of  the  gas  expanded  by  the  heat.  After  all  these  ma- 
nipulations— which  take  longer  to  describe  than  to  carry  out — 
I  place  the  apparatus  in  a  bath  of  hot  water  and  open  the  end 
of  the  tube  G  after  having  put  it  in  a  small  mercury  bath,  as 
in  the  former  apparatus.  When  the  flask  has  come  to  the  tem- 
perature of  the  boiling  water,  I  remove  the  tube  B  (whose  end 
must  have  been  previously  withdrawn  from  the  mercury),  and 
cool  the  bath.  The  mercury  then  rises  in  the  flask  ;  but  it  will 
be  easy  to  put  water  in  its  place,  when  everything  is  at  a  lower 
temperature.  The  volume  of  the  flask  and  the  volume  of  the 
water  which  has  taken  the  place  of  that  part  of  the  gas  driven 
out  by  the  heat,  are  found  in  the  way  I  have  already  described  ; 
only  it  is  necessary  in  this  calculation  to  add  to  the  weight  of 
the  empty  flask  that  of  the  cylinder  of  water  extending  from 
the  level  ac  on  the  one  hand  to  the  end  of  the  neck  of  the 
flask  on  the  other. 

I  should  be  able  to  give  still  further  details,  but  I  withhold 
them  in  order  not  to  be  too  diffuse  :  those  a  little  practiced  in 
manipulation  will  readily  supply  them.  However,  as  it  is  a  mat- 
ter of  importance,  after  what  I  have  said  about  the  effects  of 
moisture,  to  remove  it  entirely  from  the  apparatus,  I  will  de- 
scribe how  I  have  been  successful  in  doing  so. 
D  41 


MEMOIKS     ON 

If  the  flask  is  evidently  wet,  I  begin  by  drying  it  with  filter 
paper  ;  then  I  heat  it  so  as  to  evaporate  a  part  of  the  moisture 
which  it  still  may  contain,  and,  with  the  aid  of  a  bellows  to 
which  I  have  attached  a  glass  tube,  I  carry  into  its  interior  a 
current  of  air  to  drive  out  the  vapor.  These  last  operations 
being  repeated  many  times  with  the  flask  and  the  tube,  both 
become  perfectly  dry.  With  regard  to  the  mercury  which  I 
have  used  in  my  experiments,  I  have  invariably  used  what  was 
very  dry  and  pure. 

In  all  the  experiments  the  results  of  which  I  am  about  to 
give,  I  have  always  brought  back  to  the  temperature  of  melting 
ice  the  gases  whose  rate  of  expansion  I  have  been  able  to  de- 
termine with  the  apparatus  I  have  described  ;  and  for  this  pur- 
pose I  had  a  bath  where  I  kept  the  ice  and  in  which  the  flask 
was  completely  covered  after  having  been  taken  from  the  bath 
in  which  it  had  been  subjected  to  experiment,  and  here  I  left 
it  for  about  half  an  hour,  during  which  time  I  constantly  stirred 
the  bath.  The  other  fixed  temperature  which  I  resolved  upon 
for  the  same  gases,  is  that  of  boiling  water. 

I  have  made  some  experiments  at  other  temperatures  ;  but 
they  will  have  to  be  repeated,  and  moreover  they  will  become 
part  of  a  treatise  which  I  have  begun  upon  the  law  of  the  ex- 
pansibility of  gases  and  vapors  ;  I  shall  confine  myself  there- 
fore, as  I  have  said,  to  a  consideration  of  the  rate  of  expansion 
of  gases  for  a  definite  rise  of  temperature — which  will  be  that 
comprised  between  the  degree  for  melting  ice  and  that  for  boil- 
ing water.  With  respect  to  vapors,  I  shall  compare  their  rate 
of  expansion  with  that  of  gases. 

PART  IV. 

Experiments  and  Results. 

MAKING  use  of  the  two  [forms  of]  apparatus  I  have  de- 
scribed— but  more  often  the  second  than  the  first — and  avoid- 
ing all  the  sources  of  inaccuracy  which  I  could  foresee,  I  have 
found  from  six  experiments  upon  atmospheric  air,  the  six  fol- 
lowing results  :  * 

1  My  flask  held  about  350  grams  of  water. 

42 


EXPANSION    OF    GASES 

Starting  from  the  temperature  of  melting  ice,  at  that  of 
boiling  water  equal  volumes  of  atmospheric  air  represented  by 
100  had  become,  respectively  : — 

137.40  ;  137.61 ;  137.44  ;  137.55  ;  137.48  ;  137.57  ; 
the  mean  of  which  is  nearly  137.50.1 

If  the  total  increase  of  volume  be  divided  by  the  number  of 
degrees  which  produced  it,  or  by  80,  we  find,  making  the 
volume  at  0°  temperature  equal  to  unity,  that  the  increase  of 
volume  for  each  degree  is  *Tira  or  on  tne  other  hand,  ^.^ 
for  each  degree  of  the  centigrade  thermometer. 

Deluc  having  found  ^Jy  for  the  coefficient,  it  would  appear 
at  first  sight  that  our  results  are  the  same  ;  but  if  it  be  noted 
that  he  starts  from  a  temperature  of  16f  °,  while  I  start  from 
a  temperature  of  0°,  it  will  be  seen  that  our  results  are  quite 
different.  2  I  shall  later  consider  this  difference  and  show 
that  the  coefficients  of  expansion  vary  with  the  temperature 
from  which  we  set  out. 

Hydrogen  gas  produced  from  iron  by  weak  sulphuric  acid 
was  submitted  to  two  experiments  :  in  one,  through  an  eleva- 
tion of  temperature  from  that  of  melting  ice  to  that  of  boiling 
water,  100  parts  [by  volume]  became  137.49  ;  and  in  the  other, 
through  the  same  rise  of  temperature  100  parts  became  137.56. 
The  average  of  these  two  results  is  137.52 — which  differs  only 
slightly  from  the  average  result  found  for  the  expansion  of 
atmospheric  air. 

Oxygen  gas  given  off  from  the  oxygenated  muriate  of 
potash  [i.  e.,  potassium  chlorate]  was  tested  three  times  and 
gave  the  following  results  :  100  parts  became 

1  Although  the    differences    among  the  results  are  not  very  consi- 
derable, I  believe  I  could  have  made  them  very  small  had  I  been  able  to 
note  the  state  of  the  barometer  during  the  boiling  of  the  water.     How- 
ever, I  have  always  taken  care  to  note  its  temperature  at  the  moment 
of  boiling  and  I  confess  I  have  never  noticed  any  marked   variations. 
As  a  matter  of  fact  it  requires  a  change  of  an  inch  in  the  barometer  to 
produce  one  of  a  degree  in   the  boiling  point  of  water,— which  must 
occur  but  rarely.     However  that  may  be,  the  mean  result,  137.50,  must 
be  very  close. 

2  Note  by  Translator: — In  the  memoir  the  second  temperature  stated 
is  "  0°| ;  "  it  seems  evident  that  this  is  a  typographical  error. 

43 


ME  MO  IKS    ON 


137.47  ;  137.54  ;  137.45  ; 
the  mean  of  which  is  137.48. 

Nitrogen  gas  obtained  through  the  decomposition  of  am- 
monia by  oxygenated  muriatic  acid  [i.  e.  chlorine]  gave  the  fol- 
lowing five  results  :  100  parts  became 

137.42  ;  137.56  ;  137.50  ;  137.46  ;  137.55  ; 
the  mean  of  which  is  137.49. 

On  bringing  together  the  preceding  results  and  comparing 
the  expansion  of  the  gases  oxygen,  hydrogen  and  nitrogen  with 
that  of  atmospheric  air,  there  results  a  table  like  this— 


Between  the  temperature  of 
melting  ice  and  that  of  boil- 
ing water,  100  parts  of 

Suffer  an 
increase  of 

Differences 

Atmospheric  air 
Hydrogen  gas 
Oxygen  gas 
Nitrogen  gas 

37.50  parts 
37.52 
37.48 
37.49 

+  0.02 
—  0.02 
—  0.01 

The  slight  differences  observable  in  the  above  results  may 
arise  from  the  fact  that  it  is  impossible  to  make  the  conditions 
rigorously  identical  in  every  experiment,  and  as  they  amount  to 
only  two  ten-thousandths  of  the  original  volume,  we  may  safely 
conclude  that  atmospheric  air  and  the  gases  oxygen,  hydrogen 
and  nitrogen  expand  to  the  same  extent  between  the  tempera- 
ture of  melting  ice  and  that  of  boiling  water. 

In  order  to  determine  the  rate  of  expansion  of  gases  soluble 
in  water,  I  made  a  change  in  the  apparatus.  I  used  two  tubes 
TT(Fig.  2,  Plate  II)  [See  Fig.  4]  calibrated  at  the  same  time 
over  the  same  mercury  bath  AC,  by  means  of  a  very  small 
measure. 

Each  time  that  I  made  use  of  this  apparatus,  I  took  care 
that  the  quantity  of  mercury  should  be  the  same  as  when  the 
tubes  were  calibrated.  I  ought  to  say  that,  if  the  basin  which 
held  the  mercury  suffered  any  injury,  it  was  necessary  to  re- 
calibrate the  tubes  for  another  bath  ;  indeed  it  would  be  well  to 
cut  them  from  the  same  cylinder  of  glass  and  to  give  them  the 
same  height,  in  order  to  have  all  the  conditions  as  much  the 
same  as  possible. 

Into  one  of  these  tubes  I  admitted  atmospheric  air  down  to 

44 


EXPANSION    OF    GASES 


the  100th  division,  for  example,  and  into  the  other  the  gas 
whose  rate  of  expansion  I  wished  to  determine,  also  as  far  as  the 
100th  division.  I  thus  subject  to  test  100  equal  measures  of 
each  of  two  gases.  I  then  place  the  apparatus  in  a  heater 
whose  temperature  I  can  control  and  watch  the  progress  of  the 
expansion  of  the  gases.  However  great  the  care  I  have  taken  to 
observe  closely,  I  have  never 
perceived  any  difference  and 
have  always  noticed  that  the 
same  divisions  were  passed  at 
the  same  time  in  the  two  tubes. 

The  gases  I  have  thus  ex- 
amined  have  never  been  intro- 
duced directly  into  the  tubes;  I 
have  kept  them  for  some  time 
before  in  an  intermediate  vessel 
in  which  I  put  some  drying- 
agent, — for  example,  muriate  of 
lime,  [i.  e.  calcium  chloride] — 
and  made  them  pass  thence  into 
the  tubes  by  compressing  them 
with  the  aid  of  mercury  which  I 
introduced  by  means  of  a  safety 
tube  fitted  to  the  intermediate  FIG.  4. 

flask.  If  these  precautions  are  neglected,  there  will  almost 
always  result  far  too  great  an  expansion ;  we  must  therefore 
avoid  the  contamination  of  unabsorbed  moisture  or  of  any 
other  substance  capable  readily  of  assuming  the  gaseous  state. 

100  measures  of  carbonic  acid  gas  obtained  from  marble 
with  the  aid  of  sulphuric  acid  were  compared  with  100  measures 
of  atmospheric  air.  From  the  fifth  degree  up  to  the  90th  de- 
gree the  expansions  were  the  same  in  the  two  tubes. 

100  measures  of  muriatic  acid  gas  produced  with  the  aid  of 
concentrated  sulphuric  acid  from  muriate  of  soda  [i.  e.  com- 
mon salt]  thoroughly  dried  by  heat,  having  been  compared 
with  100  measures  of  atmospheric  air  from  the  3d  degree  up  to 
the  86th,  the  expansions  of  the  two  gases  were  absolutely  the 
same.  This  experiment,  as  well  as  the  preceding  one,  was  re- 
peated many  times,  and  always  gave  the  same  result. 

45 


MEMOIES    OK 

Sulphurous  acid  gas  and  nitrous  gas,  again,  showed  under 
the  influence  of  heat  the  same  expansion  as  atmospheric 
air. 

Dr.  Priestley  and  Citizens  Guyton  and  Duvernois  have  found 
very  great  expansibility  in  the  case  of  ammonia  gas.  With  tiie 
idea  of  discovering  the  cause  which  was  capable  of  vitiating 
the  results  of  their  experiments,  I  introduced  directly  into  one 
of  the  tubes  some  ammonia  gas  produced  by  the  decomposition  of 
muriate  of  ammonia  by  means  of  ordinary  lime,  and  into  the 
other  a  suitable  volume  of  atmospheric  air.  As  the  tempera- 
ture rose,  the  ammonia  gas  expanded  proportionally  more  than 
the  atmospheric  air,  in  fact  to  such  a  degree  as  soon  to  become 
twice  as  great;  yet  on  examining  the  mercury  surface  and  the 
walls  of  the  tube,  after  lowering  the  temperature,  I  noticed  a 
trace  of  liquid  and  some  crystalline  needles  which  could  be 
only  muriate  or  carbonate  of  arnmonia;  and  the  whole  disap- 
peared on  raising  the  temperature  to  a  sufficient  degree.  How- 
ever that  may  be,  I  began  the  experiment  again  by  allowing 
the  ammonia  gas  to  stand  some  time  in  an  intermediate  flask 
where  there  was  some  caustic  potash,  and  then,  from  0°  up  to 
95°,  its  expansion  followed  exactly  that  of  atmospheric  air.  I 
again  examined  the  surface  of  the  mercury  and  the  walls  of  the 
tube,  when  the  temperature  had  returned  to  0°,  but  this  time 
I  noticed  neither  liquid  nor  crystalline  needles.  This  experi- 
ment, repeated  many  times,  always  met  with  the  same  suc- 
cess. 

It  is  thus  evident,  from  what  I  have  said,  that  not  only  a  liq- 
uid, but  any  other  substance  capable  of  assuming  the  gaseous 
state  can  easily  lead  to  error;  it  is  necessary  therefore  to  avoid 
such  things  with  the  most  scrupulous  care. 

The  experiments  of  which  I  have  given  an  account  and  all  of 
which  were  made  with  great  care,  prove  without  a  doubt  that 
atmospheric  air  and  the  gases  oxygen,  hydrogen,  nitrogen,  nit- 
rous gas,  ammonia,  muriatic  acid,  sulphurous  acid  and  car- 
bonic acid  gases  expand  to  the  same  extent  for  the  same  de- 
grees of  heat;  and  that  consequently  their  greater  or  less  dens- 
ity under  the  same  pressure  and  at  the  same  temperature,  their 
greater  or  less  solubility  in  water,  and  their  individual  charac- 
ter, have  no  influence  upon  their  expansibility. 

46 


EXPANSION    OF    GASES 

In  consideration  of  this  fact  I  conclude  that  all  gases,  speak- 
ing generally,  expand  to  the  same  extent  through  equal  ranges 
of  heat;  provided  all  are  subject  to  the  same  conditions. 

These  researches  upon  the  rate  of  expansion  of  gases  nat- 
urally led  me  to  investigate  that  of  vapors;  but  expecting,  from 
the  result  of  the  above  determinations,  that  they  would  expand 
like  gases,  1  decided  to  experiment  upon  only  one  vapor,  and 
chose  that  of  sulphuric  ether  as  being  very  easy  to  work  with. 

In  order  then  to  determine  the  rate  of  expansion  of  ether  vapor 
I  made  use  of  the  two  tubes  of  which  I  have  already  spoken, 
atmospheric  air  serving  throughout  as  a  means  of  comparison. 
This  apparatus  having  been  kept  for  some  time  in  a  heater 
whose  temperature  was  about  60°,  I  admitted  ether  vapor  into 
one  of  the  tubes  and,  atmospheric  air  into  the  other,  in  such  a 
way  that  each  was  filled  to  the  same  point.  I  then  raised  the 
temperature  of  the  heater  from  60°  to  100°,  and  had  the  satis- 
faction of  seeing  that,  whether  rising  or  falling,  the  ether  va- 
por and  the  atmospheric  air  always  stood  at  the  same  division 
at  the  same  moment.  This  experiment,  which  Citizen  Berth- 
ollet  has  witnessed,  was  repeated  many  times  and  I  have  never 
been  able  to  note  any  difference  in  its  rate  of  expansion  as  com- 
pared with  that  of  atmospheric  air.  I  would  however  empha- 
size the  fact  that  a  few  degrees  above  the  boiling  point  of  ether, 
its  contraction  was  a  little  more  rapid  than  that  of  atmospheric 
air.  This  phenomenon  goes  with  one  which  many  substances 
exhibit  in  passing  from  the  liquid  to  the  solid  state,  but  which 
is  no  longer  noticeable  a  few  degrees  above  that  at  which  the 
change  is  made. 

This  experiment,  by  showing  that  ether  vapor  and  gases  ex- 
pand at  the  same  rate,  makes  it  evident  that  this  property  is  in 
no  way  dependent  upon  the  peculiar  nature  of  the  gases  and 
the  vapors  but  solely  upon  their  elastic  character,  and  conse- 
quently leads  us  to  the  conclusion  that  all  gases  and  all  vapors 
expand  to  the  same  extent  for  the  same  degrees  of  heat. 

Since  all  gases  are  expanded  to  the  same  extent  by  heat  and 
are  equally  compressible,  and  since  these  two  properties  are 
mutually  dependent,  as  I  shall  show  elsewhere,  vapors — which 
are  expansible  to  the  same  degree  as  gases — must  also  be 
equally  compressible:  yet  I  emphasize  the  fact  that  this  latter 

47 


MEMOIRS    ON 

conclusion  can  be  true  only  so  long  as  the  compressed  vapor  re- 
mains completely  in  its  elastic  state,  and  this  demands  that  its 
temperature  shall  be  high  enough  to  overcome  the  pressure 
which  would  tend  to  make  it  assume  the  liquid  state. 

I  have  quoted  Saussure — and  my  experiments  confirm  his 
view — to  the  effect  that  very  dry  air  and  air  holding  in  solution 
more  or  less  moisture  expand  at  the  same  rate;  I  am  therefore 
in  a  position  to  draw  from  all  I  have  said  the  following  con- 
clusions:— 

I.  All  gases,  whatever  their  density  or  the  quantity  of  water 
which  they  hold  in  solution,  and  all  vapors  expand  to  the  same 
extent  for  the  same  degree  of  heat. 

II.  In  the  case  of  the  permanent  gases,  the  increase  of  vol- 
ume which  each  of  them  suffers  between  the  degree  of  melting 
ice  and  that  of  boiling  water,  amounts  to  ^£-5-5  of  the  original 
volume,  for  a  thermometer  divided  in  80  parts,  or  ^^°.§^  °f  tne 
same  volume,  for  a  centigrade  thermometer. 

In  order  to  complete  this  research,  it  remains  for  me  to  de- 
termine the  law  of  the  expansion  of  gases  and  vapors,  with  the 
object  of  finding. with  its  aid  the  coefficient  of  expansion  for 
any  given  degree  of  heat,  and  of  establishing  the  true  move- 
ment of  the  thermometer.  I  am  at  work  upon  this  new  re- 
search and,  as  soon  as  it  is  concluded,  I  shall  have  the  honor  of 
laying  an  account  of  it  before  the  Institute. 


BIOGRAPHICAL  SKETCH. 

Louis  JOSEPH  GAY-LUSSAC  was  born  in  1778.  He  received 
his  scientific  education  at  the  Ecole  Polytechnique  and  the 
Ecole  des  Fonts  et  Chausse'es,  and  in  1800  became  assistant  to 
Berthollet.  The  research  upon  the  expansion  of  gases  by  heat 
was  one  of  his  first.  Like  his  contemporary,  Dalton,  he  was 
much  interested  in  the  study  of  the  atmosphere  and  in  1804 
made  analyses  of  the  air,  securing  specimens  from  various 
places — one,  at  a  height  of  over  6,000  meters,  in  a  balloon 
ascent.  The  analysis  of  water  was  also  made  at  this  time.  In 
1807  he  published  papers  upon  terrestrial  magnetism  and  the 

48 


EXPANSION     OF    GASES 

results  of  his  classic  investigation  of  the  volume-relations  of 
gases  undergoing  chemical  change.  Along  with  Thenard,  he 
studied  the  properties  of  the  metals  of  the  alkalies  and  of 
chlorine,  advocating,  with  Davy,  their  elementary  character. 
In  1809  he  became  Professor  of  Physics  in  the  Faculte  des  Sci- 
ences and  Professor  of  Chemistry  in  the  Ecole  Polytechniqne; 
in  the  same  year,  working  with  Thenard,  he  was  able  to  isolate 
boron  and,  later,  iodine.  The  latter  is  considered  one  of  his 
most  brilliant  investigations.  During  the  next  few  years  he 
published  important  memoirs  upon  the  relationships  existing  be- 
tween ethylene,  alcohol  and  ether.  In  1815  he  discovered  cyan- 
ogen and  prepared  pure  hydrocyanic  acid.  In  1815  he  devised 
the  syphon  barometer. 

Gay-Lussac's  ingenuity  frequently  made  itself  evident  in  the 
construction  of  new  forms  of  apparatus:  in  addition  to  the 
syphon  barometer,  we  owe  to  him  a  large  number  of  useful  in- 
struments constantly  employed  in  the  laboratory.  His  death 
occurred  in  1850. 


49 


THE  DETERMINATION    OF  THE  RATE  OF 
EXPANSION  OF  GASES  BY  HEAT. 

BY  J.  B.  BIOT. 

Translated  from  Volume  I,  Chapter  IX,  of  the  Author's  "  Traite 
de  Physique" 


51 


CONTENTS. 

PAGE. 

Third  Method  of  Gay-Lussac:  Apparatus     ...  53 

Need  of  excluding  moisture;  method  of  drying  apparatus  54 

Manipulation  .         .                  •• 55 

Coefficient  of  expansion  of  glass  containing -vessel      .         .  56 

Results  and  conclusions 59 


EXTRACT  FROM  BIOT'S  TREATISE   ON 
PHYSICS : 

BEING  CHAPTER  IX  OF  VOLUME  I. 

The  Determination  of  the  Rate  of  Expansion  of  Gases  by  Heat. 

THE  experiments  of  MM.  Lavoisier  and  Laplace  upon  the 
expansion  of  solid  substances  have  shown  us  that  between  the 
limits  of  [the  temperature  of]  melting  ice  and  [that  of]  boil- 
ing water,  the  expansion  of  solid  metals  is  practically  propor- 
tional to  that  of  mercury.  The  same  relation,  between  these 
limits,  exists  as  well  between  the  expansion  of  mercury  and 
that  of  dry  gases.  This  important  deduction  has  been  com- 
pletely established  by  the  experiments  which  M.  Gay-Lussac 
has  made  with  this  object  in  view,  upon  the  rate  of  expansion 
of  gases.  This  skilful  physicist  having  been  willing  to  make  ' 
known  to  me  the  details  of  his  experiments,  and  to  permit  me 
to  sketch  the  apparatus  which  he  has  devised  for  the  purpose, 
I  shall  proceed  to  describe  here  the  course  which  he  followed 
in  his  investigations  and  the  results  to  which  he  was  led. 

In  order  to  measure  with  accuracy  the  rate  of  expansion  of 
gaseous  substances,  it  is  necessary,  first  of  all,  to  introduce 
them,  in  known  quantity,  into  tubes  accurately  graduated  into 
divisions  of  equal  volume,  and  terminating  in  a  bulb  whose 
volume  should  be  considerable  as  compared  with  that  of  the 
tube.  It  is  necessary,  further,  that  they  should  be  kept  there 
under  a  known  pressure,  exposed  to  different  temperatures  and 
the  amounts  by  which  they  expand  or  contract  under  the  dif- 
ferent conditions  observed  ;  in  a  word,  it  is  necessary  to  make 
a  veritable  gas  thermometer.  Yet  although  the  statement  of 
this  operation  may  be  very  simple,  it  demands,  in  order  to  be 
accurate,  many  essential  precautions  which  we  shall  now 
discuss. 

The  first  is,  that  the  tubes  in  which  the  gases  are  contained 
must  be  perfectly  dry ;  for  we  have  already  stated  that  glass 

53 


MEMOIRS    ON 

tubes  lying  open  and  exposed  to  the  atmosphere,  become  cov- 
ered inside  with  a  slight,  imperceptible  layer  of  water  which 
heat  sets  free  by  converting  it  into  vapor.  If  one  did  not  begin 
by  removing  this  thin  layer  of  water,  the  vapor  which  it  gives 
off  at  different  temperatures  would  mix  with  the  gas  introduced 
into  the  tube  and  would  increase  its  volume  ;  and,  since  the 
amount  of  the  vapor  thus  produced  would  increase  with  the 
temperature  until  the  slight  layer  of  water  had  become  com- 
pletely removed,  it  is  evident  that  this  outside  cause  will  con- 
stantly increase  the  expansion  proper  of  the  gas,  in  proportion 
as  the  temperature  rises  :  such  is  the  error  into  which  many 
physicists  have  fallen. 

The  only  way  to  avoid  this  difficulty  is  to  drive  out  this 
slight  film  of  moisture  by  heating  the  tube  until  it  is  changed 
to  vapor ;  but  in  order  that  the  air  may  not  enter  again,  it  is 
necessary  to  fill  the  tube  with  mercury,  which  is  made  to  boil 

T  T 


FIG.  1. 

there,  as  in  a  thermometer  ;  and — which  is  important  to  notice 
— whether  this  boiling  removes  or  not  the  whole  of  the  film 
adhering  to  the  glass,  at  least  it  can  no  more  give  off  vapor 
when  the  tube  is  kept  at  any  temperature  less  than  that  at 
which  mercury  boils.  This  is  the  first  precaution  M.  Gay-Lus- 
sac  has  taken. 

Next,  in  order  to  introduce  only  air  or  dry  gases  into  the 
tube,  he  connects  to  its  open  end  another,  larger  tube  TTy 
Fig.  66  [Fig.  1],  which  may  be  regarded  as  a  kind  of  receiver 
intended  to  hold  the  gas.  This  tube  is  partly  filled  with  bits 
of  muriate  of  lime  [i.  e.,  calcium  chloride]  or  of  any  other  salts 
capable  of  absorbing  moisture.  It  is  even  possible  to  produce 
a  vacuum  in  it  in  order  to  introduce  the  gas  without  admixture 
of  air.  Then  in  order  to  let  a  definite  quantity  enter  the  tube, 
M.  Gay-Lussac  makes  use  of  a  very  fine  iron  wire  previously 
introduced  into  the  bore.  He  inclines  the  tube  or  turns  it  up- 
side down,  and  thus  removes  a  large  part  of  the  mercury  which 
it  contains,  whose  place  is  taken  by  a  definite  volume  of  gas 
represented  by  GG,  Fig.  67,  [Fig.  2].  With  care,  it  can  be  ar- 
ranged to  have  only  a  short  column  of  mercury  M  which  acts 

54 


EXPANSION    OF    GASES 

as  a  piston,  and  all  the  space  GG,  from  this  point  to  the  bulb 
of  the  tube  is  filled  with  the  dry  gas  which  has  been  intro- 
duced. If  he  is  employing  atmospheric  air,  there  is  no  need  of 
producing  a  vacuum  in  the  receiver  TT;  the  air  should  be 
allowed  to  remain  some  time  in  contact  with  the  salts,  after 
which  it  is  introduced  into  the  tube  GT,  as  we  have  described. 


FIG.  2. 

The  gas  having  been  introduced,  it  remains  only  to  try  the 
effect  of  various  known  temperatures  successively  upon  it ;  for 
this  M.  Gay-Lussac  made  use  of  a  metal  vessel  AB,  Fig.  67  [Fig. 
2]  rectangular  in  shape,  the  bottom  of  which  fits  upon  a  fur- 
nace of  the  same  size.  Water  is  put  in  this  vessel  and  is  heated 
to  different  temperatures.  A  thermometer  F}  placed  vertically 
in  this  water  and  whose  stem  projects  above  the  cover  of  the 
vessel,  serves  to  indicate  its  temperature  approximately  and  to 
show  if  it  is  necessary  to  increase  or  diminish  the  heat. 

The  tube  TG,  however,  which  contains  the  gas,  must  not  be 
put  in  the  water  in  this  position;  for  we  have  already  shown 
by  experiment  that  the  different  horizontal  layers  of  a  liquid, 
which  is  being  heated  from  the  bottom,  are  not  at  the  same 
degree  of  temperature.  Thus,  in  order  to  know  exactly  that 
[temperature]  which  is  producing  an  effect  upon  the  gas,  the 
tube  which  contains  it  must  be  fixed  in  a  horizontal  position, 
as  Fig,  67  [Fig.  2]  shows  it;  then  its  temperature  may  be 
accurately  determined  by  an  excellent  thermometer  tt  placed 
opposite  it  in  the  same  layer  and  likewise  fixed  in  a  horizontal 
position. 

55 


MEMOIRS    ON 

But  we  have  stated  that  the  vessel  was  of  metal;  how  then 
observe  through  its  walls  the  divisions  of  the  thermometer  it 
and  the  movable  point  G  of  the  graduated  tube  to  which  at 
any  moment  the  gas-volume  extends  ?  The  point  G  and  the 
stem  t  of  the  thermometer  cannot  be  kept  continually  outside 
the  hot-water  bath,  for  then  these  parts  respectively,  being  no 
longer  at  the  temperature  of  the  bath,  would  introduce  an 
error  into  the  determination.  Yet  one  can,  without  inconveni- 
ence, draw  out  the  tubes  from  time  to  time,  during  the  short 
interval  required  to  observe  them:  this  M.  Gay-Lussac  accom- 
plished in  a  very  simple  way.  The  openings  00'  through  which 
the  tubes  pass  into  the  vessel  are  closed  with  corks  pierced 
along  their  axes  with  a  hole  through  which  the  tube  in  either 
case  can  slip  with  some  friction.  Is  it  desired  to  observe  the 
condition  of  the  gas  GG?  The  tube  TG  is  drawn  out  until 
the  end  J/of  the  short  column  of  mercury  comes  into  sight  at 
the  opening  0.  It  can  then  be  seen  at  what  division  of  the 
tube  it  stands,  and  the  volume  of  the  gas  at  this  moment  is 
known.  Is  it  desired  to  note  the  temperature  at  the  same 
time?  The  stem  is  similarly  drawn  out  until  the  end  t  of  the 
mercury  column  appears  at  the  opening  0',  and  then  the  divi- 
sion of  the  thermometer  to  which  this  corresponds  indicates 
the  temperature  at  the  time  of  the  horizontal  layer  in  which 
the  gas  has  been  placed. 

Thus  at  each  moment  the  temperature  of  the  gas  is  known 
in  the  most  exact  way.  Putting  water  at  0  °  at  first,  therefore, 
in  the  vessel,  then  raising  the  temperature  by  successive  steps 
to  that  of  boiling;  or,  vice  versa,  returning  from  boiling  to  the 
melting  point  of  ice;  the  movement  of  the  gas  and  that  of  the 
thermometer  can  be  compared  with  accuracy — that  is  to  say,  at 
any  time,  by  the  divisions  marked  upon  the  tube,  the  apparent 
volume  of  the  mercury  and  the  apparent  volume  of  the  gas 
may  be  known;  but  to  have  the  real  volumes,  it  is  still  necessary 
to  take  into  account  the  expansion  of  the  glass  of  which  the 
tubes  are  made. 

To  study  this  effect  properly,  let  us  start  from  some  definite 
temperature — for  example,  that  of  melting  ice.  Let  us  desig- 
nate by  F  the  number  of  divisions  which  the  gas  then  occu- 
pies in  the  glass  vessel  that  encloses  it,  and  let  us  make  use  of 

56 


EXPANSION    OP    GASES 

this  number  to  express  its  volume.  On  the  temperature  rising 
t  degrees,  the  volume  of  the  gas  will  increase  and  become 
F(l-hf),  designating  by  Jits  cubical  expansion  from  0°  to  t 
degrees,  and  this  is  the  unknown  quantity  we  are  looking  for. 
Let  F  be  the  number  of  divisions  it  now  occupies  in  the  tube. 
As  the  latter  expands  each  of  its  divisions  has  in  reality  a  differ- 
ent value  from  that  which  it  had  at  the  initial  temperature, 
and  if  the  cubical  expansion  of  the  material  of  the  tube,  for  one 
degree  of  the  thermometer,  is  represented  by  K,  V'  divisions 
at  the  temperature  t  will  be  equal  to  V  (1+Kt)  of  the  original 
divisions.  This  will  therefore  be  the  actual  expression  of  the 
new  volume  of  the  gas  stated  in  terms  of  the  original  divisions 
— that  is  to  say,  we  shall  have 

F  (!+«*)       F  (1+JR), 
from  which  we  obtain 

._  V-V      VKt 
~~V~       ~T~ 

The  first  term,     ~    ,  is  the  cubical  expansion  for  a  volume 

equal  to  unity,  assuming  the  vessel  did  not  expand;   and  the 

V'Kt 
second  term,^^-,  is  the  correction  which  must  be  made  in  the 

first  result  on  account  of  the  expansion  of  the  vessel. 

F  is  determined  at  the  beginning  of  the  experiment;  it  is 
the  number  of  divisions  occupied  by  the  gas  at  the  initial 
temperature;  subsequently,  at  other  temperatures,  the  reading 
gives  F',  the  number  of  divisions  the  gas  occupies  at  any  given 
moment.  Moreover  K  is  found  from  the  expansion  of  solids; 
thus  the  whole  second  number  of  our  equation  is  known  and, 
consequently,  on  substituting  their  values  for  F,  F,  K,  t,  the 
expansion  6  is  found  just  as  it  would  have  been  determined  in 
a  vessel  upon  which  [a  change  of]  temperature  produced  no 
effect. 

It  only  remains  to  take  account  of  the  pressure  to  which 
the  gas  is  subjected,  for  we  have  seen  that  the  volumes  which 
a  given  gas  will  occupy,  at  a  given  temperature,  are  inversely 
proportional  to  the  pressures  to  which  it  is  subjected.  Here,  dur- 
ing the  experiments,  the  receiver,  TT,  Fig.  67  [Fig. 2]  remains 
always  open;  the  pressure  of  the  atmosphere  thus  acts  freely 
upon  the  short  column  of  mercury,  M9  close  to  the  gas  GG. 
E  57 


MEMOIRS     ON 

If  the  tube  TG  were  vertical  or  inclined  to  the  horizon,  the 
weight  of  this  short  column  M  would  also  act  upon  the  gas; 
but  the  tube  being  horizontal,  this  weight  is  entirely  carried  by 
the  glass  tube.  The  short  column  M  opposes  no  pressure,  no 
resistance  to  the  motion  of  the  gas  —  unless,  perhaps,  that  re- 
sulting from  its  friction  against  the  inner  walls  of  the  glass 
tube;  and  this  force  is  so  small,  when  the  column  is  short,  that 
it  may  be  neglected.  The  weight,  then,  of  the  atmosphere  is 
the  only  force  which  weighs  upon  the  gas  GG,  and  it  is  deter- 
mined by  observing  the  height  of  the  barometer  at  the  time 
of  taking  the  readings.  If  this  pressure  remains  constant 
throughout  the  experiment,  the  corresponding  volumes  of  gas 
and  of  mercury  may  be  directly  compared  with  one  another; 
but,  if  it  varies,  all  the  readings  must  be  reduced  to  one  pres- 
sure —  which  is  easy,  making  use  of  Mariotte's  Law. 

Thus,  let  p  be  the  atmospheric  pressure  observed  at  the 
beginning  of  the  experiment  and  at  the  initial  temperature, 
when  the  gas  in  the  vessel  occupies  a  number  Fof  divisions. 
Let  us  suppose  that  it  is  desired  to  reduce  this  volume  to  what  it 
would  have  been  under  the  constant  pressure  of  0.76  m.,  to  which 
we  refer  all  observations.  Then,  according  to  Mariotte's  Law, 
the  volume  Fmust  be  reduced  inversely  as  tke  pressures  ;  that 

is  to  say,  in  place  of  Fwe  have  ^~. 

In  the  same  way,  if  we  assume  the  pressure  of  the  atmos- 
phere to  bey,  when  the  gas  is  at  the  temperature  t,  and  that 
it  occupies  in  the  vessel  a  number  of  divisions  represented  by 
F,  this  number,  under  a  pressure  of  0.76  m.,  but  at  a  tem- 

perature  t,  will  become 


. 

Therefore  to  arrive  at  the  expansions  which  would  have  re- 
sulted if  the  pressure  had  remained  constant  and  equal  to  0.76, 

V  n  V  n' 

we  must  substitute  for  Fand  F  in  our  formula,  —    and    -; 
then  the  value  of  <5  becomes 

.       pf  V'-p  V    p' 
' 


PV  '          P   V 

Use  must  be   made  of  this  formula  in  order  to  take  account 
of  all   the  attending  conditions.     When  the  pressure  is  coh- 

58 


EXPANSION    OF    GASES 

sfcant  throughout  the  experiment,  we  have  p  =  p',  and  we  fall 
back  upon  the  formula  which  we  had  found  at  first. 

When  d  shall  have  been  thus  determined  for  an  interval  of  t 
degrees,  the  experiment  is  begun  again  or  is  continued  for  an 

interval  %t,  3t, ;  and  by  comparison  of  the  values  of  6  with 

one  another,  it  may  be  known  whether  the  rate  of  expansion 
is  uniform  or  variable.  For,  if  it  is  uniform,  the  successive 
expansions,  6,  2<f,  3<*, ,  will  be  proportional  to  the  differ- 
ences in  temperature  ;  but  if  the  rate  of  expansion  is  increas- 
ing or  decreasing,  this  proportionality  will  not  obtain.  Per- 
forming the  experiment  in  this  way,  with  all  the  precautions 
we  have  described,  repeating  it  a  great  number  of  times,  as 
well  with  atmospheric  air  as  with  the  different  gases,  M.  Gay- 
Lussac  arrived  at  the  following  results  : 

All  the  permanent  gases,  subjected  to  equal  [changes  of] 
temperature,  under  the  same  pressure,  expand  by  exactly  the 
same  amount. 

The  amount  of  their  common  expansion,  from  the  tem- 
perature of  melting  ice  up  to  that  of  100  degrees  of  the 
centigrade  thermometer,  is  equal  to  0.375  of  their  original 
volume  at  0°,  assuming  pressure  to  be  constant. 

Between  these  two  limits  the  expansion  of  a  gas  is  exactly 
proportional  to  the  expansion  of  mercury ;  whence  it  follows 
that,  for  every  degree  of  the  centigrade  thermometer,  and 
under  a  given  pressure,  all  gases  expand  by  an  amount  equal  to 
0.00375  of  the  volume  which  they  occupy  at  the  temperature 
of  melting  ice. 

These  results  had  been  obtained  almost  simultaneously  by 
Mr.  Dalton,  the  brilliant  physicist  of  Manchester  ;  but  the 
work  of  M.  Gay-Lussac  was  completed  in  France  before  that  of 
the  English  physicist  could  have  been  known.  Mr.  Dalfcon 
finds  the  actual  expansion  slightly  different  from  that  [found]  by 
M.  Gay-Lussac.  He  makes  it  equal  to  0.372,  and  finds  that,  for 
a  given  expansion  of  mercury,  that  of  atmospheric  air  is  a  little 
less  in  proportion  and  that  this  difference  increases  as  the 
temperature  rises.  Yet  however  great  the  skill  of  this  philos- 
opher in  experimental  research,  we  believe  that  the  result  of 
M.  Gay-Lussac  may  be  considered  as  still  more  accurate,  as 
much  by  reason  of  the  endless  precautions  he  has  taken  to 

59 


MEMOIRS    ON 

obtain  it,  as  because  it  agrees  very  well  with  all  the  other 
physical  determinations  in  which  there  is  need  to  use  the  figure 
for  the  absolute  rate  of  expansion  of  gases. 

It  would  not  be>out  of  the  way  to  note  on  the  other  hand 
that  the  ratio  0.00375  is  exactly  the  one  that  has  been  found 
for  atmospheric  air  by  the  distinguished  astronomer  Tobie 
Mayer,  who  appears  to  have  been  as  skilful  in  the  art  of 
physical  experiment  as  in  that  of  making  and  coordinating 
astronomical  observations.  M.  Gay-Lussac  has  stated  in  his 
memoir  that  our  renowned  physicist,  M.  Charles,  had  long 
before  discovered  the  equal  rate  of  expansion  of  gases  and  had 
made  it  apparent  by  an  apparatus  constructed  for  his  splendid 
museum;  but  he  had  made  no  attempt  to  measure  accurately 
the  absolute  rate  of  their  expansion.  Doubtless  we  have  reason 
to  regret  the  many  other  results  of  observation  and  experiment 
which  M.  Charles  had  intended  for  use  only  in  his  public 
lectures  and  which  have  never  been  published. 

M.  Gay-Lussac  is  in  the  same  way  convinced  that  the  gaseous 
substances  produced  by  the  evaporation  of  liquids  expand  at 
the  same  rate  as  gases,  so  long  as  they  do  not  become  con- 
densed to  liquid  form.  To  prove  this,  he  removed  the  drying- 
salts  from  the  receiver  TT,  introduced  into  the  tube  TG  gases 
which  had  not  been  dried  and  consequently  were  charged  with 
moisture  which  could  there  take  the  form  of  vapor  :  moisture 
which  the  drying-salts  would  take  up  with  increase  of  weight. 
By  this  means  the  space  GG  becomes  filled  with  a  mixture  of 
gas  and  aqueous  vapor  ;  and  this  mixture,  raised  to  different 
higher  temperatures  in  succession,  expands  exactly  as  would  an 
equal  volume  of  dry  gas.  But  one  must  not  look  for  the  same 
law  on  lowering  the  temperature  below  the  point  at  which  the 
gas  was  introduced  ;  for  we  shall  prove  later  on,  that  a  definite 
volume  of  gas  at  a  given  temperature  can  hold  only  a  certain 
limited  amount  of  water  in  the  form  of  vapor,  whence  it  follows 
that  if  it  is  thus  saturated  with  aqueous  vapor  at  a  given  degree 
of  the  thermometer  and  the  temperature  is  lowered,  a  portion 
of  this  vapor  will  be  condensed  to  the  liquid  state.  That  part 
which  becomes  liquid,  occupying  a  far  smaller  volume,  will 
decrease  the  total  volume  of  gas,  will  diminish  its  tension  and, 

60 


EXPANSION    OF    GASES 

as  a  result  of  this  double  effect,  will  cause  an  apparent  variation 
in  the  laws  of  expansion. 

M.  Gay-Lussac  has  in  the  same  way  studied  the  rate  of  ex- 
pansion of  ether  vapor  ;  he  finds  it  the  same  as  that  of  gases, 
— which  leads  to  the  belief  that  the  conclusion  holds  good  for 
all  kinds  of  vapors,  so  long  as  they  remain  in  the  gaseous 
state. 

With  the  aid  of  the  results  we  have  just  described,  we  can 
answer  with  accuracy  all  physical  questions  which  might  be 
asked  concerning  the  volume  of  a  given  quantity  of  gas  sub- 
jected in  turn  to  various  pressures  and  to  various  temperatures. 


61 


RESEARCHES    UPON    THE     RATE    OF    EX- 
PANSION OF  GASES. 

BY  HENRI  VICTOR  KEGNAULT. 

From  the  Annales  de  Chimie  et  de  Physique,  3d  Series,  volume 
4,  pages  5 — 67  (1842).  Translated  into  German,  Poggendorff's 
Annalen,  volume  55,  pages  391 — 414  and  557 — 584.  Also  con- 
tained in  somewhat  altered  form  in  the  Memoir es  de  V  Academie 
des  Sciences,  volume  21,  pages  15 — 120  (1847). 


63 


CONTENTS. 

PAGE 

Discussion  of  Rudberg's  researches    .                .        .        .  65 

"            Dalton's        "            .     -  .        .        .        .  71 

First  Series  of  determinations : 

Apparatus  and  manipulation       .        .        .        .  74 

Calculation  of  results   ......  79 

Sources  of  possible  error 80 

Results 81 

Second  Series  of  determinations : 

Apparatus  and  manipulation      ....  82 

Calculation  of  results   ......  86 

Results  with  the  several  bulbs        ....  87 

Third  series  of  determinations     Expansion  with  constant 

volume,  I : 

Apparatus  and  manipulation       .  89 

Calculation  of  results 92 

Results 93 

Disadvantages  of  the  method        ....  95 

Fourth  Series  of  determinations :  Expansion  with  constant 

volume,  II : 

Apparatus  and  manipulation      ....  96 

Calculation  of  results  .         .         .         .         .         .  99 

Use  of  'apparatus  at  higher  pressures           .        .  100 

Attempt  to  use  Gay- Lussacs  method          ....  101 

Discussion  of  possible  sources  of  error  in  results       .         .  103 

(a]  Expansion  of  glass 103 

(I)  Barometric  readings 104 

(c)  Temperature  determinations  ....  106 

Coefficient  of  Expansion  of  gases  other  than  Air: 

Method 107 

Results 109 

Sources  of  gases 110 

Application  of  Fourth  Method  to  Carbon  dioxide       .         .  113 

"                    "         "         Sulphurous  acid  gas          .  113 

Direct  comparison  of  two  gases  by  Fourth  Method     .         .  116 

Biographical  Sketch 120 

64 


RESEARCHES  UPON  THE  RATE  OF  EXPAN- 
SION OF  GASES. 
BY  VICTOR  KEGNAULT. 
PART  I. 

Upon  the  Rate  of  Expansion  of  Atmospheric  Air. 

THERE  is  no  numerical  quantity  in  physics  which  has  been 
submitted  to  a  greater  number  of  experimental  determinations 
than  the  coefficient  of  expansion  of  air,  and  yet  we  cannot  say 
that  up  to  the  present  time  this  coefficient  is  known  with  suf- 
ficient accuracy. 

The  experiments  of  the  older  physicists  gave  such  diverse 
numbers  that  it  was  impossible  to  draw  a  satisfactory  conclusion  ; 
most  of  the  conditions  which  affect  the  phenomenon  [of  gas  ex- 
pansion] were  entirely  unknown. 

The  brilliant  experiments  of  M.  Gay-Lussac  upon  the  rate  of 
expansion  of  gases  seemed  bound  to  put  an  end  forever  to  the 
uncertainty  of  physicists.  M.  Gay-Lussac  showed  by  a  great 
many  experiments  that  the  coefficient  of  expansion  between  0° 
and  100  °  was  the  same  for  all  gases,  and  for  vapors  so  long  as 
they  are  kept  a  little  above  their  points  of  condensation,  and 
that  its  value  was  0.375.  This  coefficient  was  adopted  by  all 
physicists  and  used  in  computations,  until  within  the  last  few 
years  a  Swedish  physicist,  M.  Eudberg,  threw  doubt  upon  its 
accuracy.  By  a  series  of  carefully  conducted  experiments  Rud- 
berg  sought  to  show  that  the  coefficient  of  M.  Gay-Lussac  was 
too  high  and  that  its  true  value  must  be  between  364  and  365. 

As  Rudberg's  work  has  never  appeared  in  France,  it  would 
seem  as  well  to  give  an  abstract  of  it  here. 

Rudberg  has  published  two  memoirs  upon  the  coefficient 
of  expansion  of  air.  In  the  earlier  (PoggendorfFs  Annalen, 
Volume  XLI)  he  uses  for  its  determination  a  species  of  air- 
thermometer  formed  of  a  bulb  of  glass  [capable  of]  enclosing 
from  120  to  150  grams  of  mercury  and  fused  to  a  capillary  tube. 
A  beginning  is  made  by  filling  this  apparatus  with  dry  air. 

65 


MEMOIRS    ON 


For  this  purpose  the  open  [end  of  the]  capillary  is  inserted  in 
a  tube  filled  with  bits  of  calcium  chloride.  The  bulb  is 
thoroughly  heated  with  an  alcohol  lamp,  then  is  allowed  to 
cool.  After  repeating  this  operation  fifty  or  sixty  times  there 
is  nothing  but  dry  air  in  the  bulb. 

At  other  times  he  placed  the  chloride-tube  in  communication 
with  an  air-pump  and  produced  a  vacuum  in  it  fifty  or  sixty 
times  in  succession,  allowing  the  air  to  return  each  time. 
These  two  methods  of  drying  were  employed  indifferently; 
they  never  gave  [results]  that  differed  noticeably. 

The  bulb,  full  of  dry  air  and  always  fitted  with 
its  calcium-chloride  tube,  was  placed  in  a  vessel 
AB  in  which  water  was  boiling  (Fig.  I),  of  such 
size  that  the  bulb  and  capillary  tube  were  com- 
pletely surrounded  by  the  vapor.  After  the  water 
had  boiled  for  three  quarters  of  an  hour  or  an 
hour,  the  calcium-chloride  tube  was  removed  and, 
ten  minutes  later,  the  drawn-out  point  of  the 
tube  was  sealed  with  a  flame,  and  at  the  same 
time  the  height  of  the  barometer  was  read. 

The  bulb  was  weighed  upon  a  very  delicate 
balance  ;  it  was  then  fixed  in  the  apparatus  [shown 
The  capillary  tube  passes  through  a  hole  in  a  metal 
capsule  abc  fastened  to  the  upright  AB.  The  arm  CD  is 
lowered  until  the  point  of  the  capillary  tube  dips  deep  enough 
in  the  small  mercury-bath  EFGH.  The  point  of  the  tube  is 
broken  off  and  the  mercury  rises  into  the  bulb.  The  latter  is 
surrounded  with  crushed  ice  placed  in  the  capsule  ale;  the  water 
formed  by  the  melting  of  the  ice  flows  off  through  the  little  tube 
/.  The  bulb  is  thus  kept  at  0°  for  at  least  two  hours,  the  ice 
being  renewed  as  fast  as  it  melts.  The  end  of  the  capillary 
tube  is  then  stopped  by  means  of  a  little  soft  wax  held  in  a  small 
iron  spoon,  and  at  the  same  time  the  height  of  the  barometer 
is  recorded. 

The  snow  is  then  removed  and  a  measurement  made  of  the 
height  of  the  raised  [column  of]  mercury.  Eudberg  used  for 
this  purpose  the  apparatus  KML  consisting  of  a  vertical 
standard  supported  by  a  tripod  with  levelling-screws.  Up  and 
down  this  stem  travels  an  arm  Imo  carrying  a  cylindrical  ring  gn 

66 


FIG.  1. 

in]  Fig.  2. 


EXPANSION    OF    GASES 

whose  lower  edge  is  exactly  horizontal.  This  ring  is  lowered 
until  its  lower  edge  coincides  with  the  level  of  the  mercury  in 
the  bulb.  At  the  same  time  the  screw-rod  KS  is  lowered  until 
its  point  reaches  the  level  surface  of  the  mercury  in  the  bath. 
The  apparatus  KML  is  then  removed  and  the  distance  from 
the  ring  to  the  point  is  measured  with  the  aid  of  a  graduated 
rule. 

The  bulb  is  weighed  with  the  mercury  which  it  contains, 
after  the  little  piece  of  wax  has  been  removed. 

The  thermometer  tube  is  bent  by  means  of  a  lamp  in  such  a 
way  that  its  open  end  can  dip  in  a  small  dish  full  of  mercury. 
The  whole  apparatus  is  filled  with  mercury  which  is  carefully 


FIG.  2. 

heated  until  it  boils.  After  it  has  cooled  down  again,  the 
bulb  and  tube  are  covered  with  crushed  ice  so  that  they  may 
become  completely  filled  with  mercury  at  0°.  The  bulb  is 
then  removed,  care  being  taken  to  catch  in  a  small  capsule  the 
mercury  which  escapes  on  account  of  expansion,  and  placed  in 
the  boiler,  the  mercury  which  flows  out  being  caught  in  the 
same  little  capsule.  This  mercury  is  carefully  weighed,  as  is 
also  that  which  has  remained  in  the  bulb.  We  thus  have  the 
total  weight  of  mercury  which  filled  the  apparatus  at  0°,  and 

67 


MEMOIBS    ON 

all  the  data  necessary  for  calculating  the  coefficient  of  expan- 
sion of  the  glass.1 

The  glass  used  for  Kudberg's  apparatus  was  a  Swedish  pot- 
ash glass  of  Reymira  make.  Its  coefficient  of  expansion  be- 
tween 0°  and  100°  was  found  to  be  0.002285  as  a  mean  of 
twenty-four  experiments,  the  extreme  figures  of  which  are 
0.002256  and  0.002321. 

The  first  three  experiments  to  determine  the  coefficient  of 
expansion  of  air  were  made  without  bringing  the  air  to  0° ;  the 
bulb  was  merely  placed  in  a  cylinder  full  of  water  whose  tem- 
perature was  taken  with  a  thermometer.  The  three  experi- 
ments gave  the  following  numbers: 

0.3633 

0.3617 

0.3623 

Mean  =  0.3624 

Rudberg  does  not  consider  these  experiments  very  accurate, 
(1)  because  the  temperature  of  the  water  surrounding  the  bulb 
was  never  perfectly  stationary,  but  varied  to  a  noticeable  ex- 
tent during  the  experiment;  (2)  because  the  difference  of  tem- 
perature was  not  100°  but  only  90°.  The  experiments  made 
with  cooling  of  the  air  to  0°,  gave: 

0.3643 

0.3654 

0.3644 

0.3650 

0.3653 

0.3636 

0.3651 

0.3643 

0.3645 

Mean  =  0.3646 

These  experiments  were  made  under  very  diverse  barometric 
pressures  ;  in  fact,  the  height  of  the  barometer  varied  from 
742.77  to  779.85.  Consequently,  the  temperature  to  which  the 
air  was  heated  varied  from  99.89°  to  100.73°.  The  height  of 

f1  Note  by  Translator.— Kudberg's  method  and  apparatus  are  similar, 
in  all  essential  points,  to  those  of  Dulong  and  Petit  in  their  comparison 
of  the  air  thermometer  and  the  mercury  thermometer.  See  page  3.] 

68 


EXPANSION     OF    GASES 

the  mercury  column  drawn  up  into  the  apparatus  varied  from 
35  mm.  to  166.5  mm. 

Rudberg  then  discusses  the  causes  which  could  introduce 
constant  errors  in  his  results.  He  states  that  capillarity  could 
not  produce  a  noticeable  effect  in  his  apparatus  because  it  was 
acting  in  a  surface  of  mercury  of  about  two-thirds  of  an  inch 
diameter.  The  friction  of  the  mercury  against  the  walls  of  the 
capillary  tube  produced  no  effect:  otherwise  differences  would 
have  been  noticed  among  the  experiments  where  the  height  [of 
the  column]  of  the  mercury  drawn  up  varied  from  35  mm.  to 
166  mm. 

Eudberg  made,  further,  two  experiments  with  large  glass 
tubes  of  §-inch  diameter  and  8  inches  length.  These  experi- 
ments he  did  not  consider  as  accurate  as  the  earlier  ones,  since 
he  could  not  boil  the  mercury  in  this  form  of  apparatus. 
They  gave  the  two  figures 

0.3646 
0.3662 


Mean  =  0.3654 

Two  experiments  made  with  air  which  had  not  been  dried 
gave  0.3840  and  0.3902,  which  gives  an  idea  of  the  influence  of 
moisture  upon  the  coefficient  of  expansion.  The  same  appara- 
tus, having  been  dried  again  with  care  and  filled  with  dry  gas, 
gave  0.3652. 

In  his  second  memoir  (Poggendorff's  Annalen,  Volume 
XLIV),  Rudberg  gives  a  series  of  experiments  made  by  means 
of  a  special  apparatus  having  for  its  object  the  determination 
of  the  tension  which  a  given  quantity  of  dry  air  exhibits  at  0° 
and  at  100°;  this  quantity  always  occupying  the  same  volume, 
allowance  being  made  each  time  for  the  expansion  of  the  glass. 

This  apparatus  is  represented  in  Fig.  3.  It  consists  of  a 
cylinder  AB  filled  with  dry  air  and  communicating  with  a 
second  tube  dC  by  means  of  a  capillary  tube  Bbd.  The  tube 
dC  is  cemented  into  the  cover  of  a  box  containing  a  leather 
pouch  filled  with  mercury,  the  volume  of  which  can  be  re- 
duced, as  in  the  case  of  barometers,  by  means  of  the  screw  M. 
A  barometer-tube  about  50  centimeters  high  is  cemented  into 

69 


MEMOIRS     ON 

the  same  cover.  By  means  of  the  screw  the  mercury  is  made 
to  rise  in  the  tubes.  Upon  the  vertical  part  of  the  tube  Id  a 
very  fine  scratch  is  made  at  a.  The  mercury  is  forced  up  to 
this  mark  by  means  of  the  screw,  (1)  when  the  reservoir  A B  is 
cooled  to  0°  by  the  aid  of  ice  ;  (2)  when  it  is  heated  to  100°. 


FIG.  3. 


The  volume  of  the  air  thus  remains  the  same  at  the  two 
temperatures,  if  the  expansion  of  the  glass  be  left  out  of  ac- 
count. In  order  to  measure  the  heights  of  the  mercury  in  the 
two  tubes,  there  is  placed  directly  behind  these  tubes  a  brass 
rule  EPRND,  graduated  in  millimeters,  the  divisions  of  which 
on  the  lower  portion,  from  a  to  b,  have  been  extended  enough 
to  pass  behind  both  of  the  tubes  at  one  time.  The  difference 
in  height  between  a  and  the  meniscus  of  the  mercury  in  ED 
can  thus  be  easily  determined. 

The  reservoir  AB  was  thoroughly  dried  before  cementing 
the  tubes  into  the  box.  To  this  end,  the  lower  portion  of  the 

70 


EXPANSION    OF    GASES 

tube  dC  was  drawn  out  to  a  point  and  connected  with  a  very 
large  tube  filled  with  calcium  chloride,  which  in  turn  was  con- 
nected with  a  pump.  The  air  having  been  exhausted  about 
fifty  times  and  replaced  by  dry  air,  the  drawn-out  tip  is  closed 
by  means  of  a  lamp.  The  tube  dC  was  fitted  into  the  box 
filled  with  dry  mercury,  and  when  this  tube  was  firmly  ce- 
mented in  place,  its  point  was  broken  off  below  the  surface  of 
the  mercury. 

The  capillary  depression  at  a  was  determined  by  a  direct  ex- 
periment before  the  narrow  tube  Bbd  had  been  fused  to  the 
reservoir  AB.  This  depression  had  been  found  to  be  18.5  mm. 

The  calculation  of  the  experiment  is  extremely  simple. 
When  the  air  is  cooled  to  0°,  let 

ff  =  the  barometric  pressure, 
h'  =  the  difference  of  level  aa, 
e  =  the  capillary  depression  at  «; 
we  then  have  for  the  tension  of  the  air,  H'  +  7^'  —  e. 

When  the  air  is  heated  to  the  temperature  Tby  means  of  [the 
vapor  of]  boiling  water,  we  have  for  its  tension,  H"  +  h"  —  e. 
Hence 


Twelve  experiments  made  according  to  this  method  gave  the 
following  figures  : 

0.3640  0.3643 

0.3648  0.3648 

0.3641  0.3653 

0.3648  0.3640 

0.3640  0.3664 

0.3656  0.3645 

Mean  =0.3645  7. 

This  mean  is  the  same  as  that  found  by  the  former  method  ; 
Rudberg  concludes  that  the  expansion  of  air  from  0°  to  100° 
must  be  between  0.364  and  0.365. 

Rudberg  closes  his  second  memoir  with  an  important  state- 
ment which  had  already  been  made  by  Gilbert  in  1803  (Gilbert's 
Annalen,  Volume  XIV,  page  267),  but  which  has  since  been 
completely  forgotten,  namely,  that  the  experiments  of  Mr. 
Dalton  and  M.  Gay-Lussac  which  have  been  looked  upon  as 

71 


MEMOIRS    ON 

having  given  almost  identical  results,  on  the  contrary  differ  a 
good  deal.  In  fact,  in  Dalton's  memoir1  taken  from  the 
Memoirs  of  the  Manchester  Society  (Gilbert's  Annalen,  Vol- 
ume XII,  page  313),  it  is  stated,  "  I  found  from  many  deter- 
minations that  1000  parts  of  atmospheric  air,  under  the  ordin- 
ary pressure  of  the  atmosphere,  expand  between  55°  F.  and 
212°  F.,  so  as  to  form  a  volume  of  1321  ;  which  gives,  after 
adding  4  parts  for  the  expansion  of  the  glass,  an  expansion  of 
325  parts  for  a  difference  of  temperature  of  157°  of  the  Fah- 
renheit scale." 

It  is  evident  that  the  volume  of  air  which  is  here  regarded  as 
unity  is  that  which  the  air  had  at  55°  F.  or  12.78°  C.  If  on 
the  other  hand  we  consider  as  unity  the  volume  of  the  air  at 
0° ,  and  if  we  denote  by  lOOa  the  expansion  between  0  °  and  100° , 
the  results  of  Dalton  give  : 

1  + 12.78  a  :  1  +  100  a  : :  1000  : 1325  ;  hence 
100  a  =  0.892. 

This  is  therefore  the  real  result  of  Dalton's  experiments.2 
Dalton  does  not,  however,  seem  to  have  been  aware  of  the  error 
which  had  crept  into  his  calculations,  for  he  says  in  his  "New 
System  of  Chemical  Philosophy  "8  :  "The  volume  of  the  air, 
according  to  the  experiments  of  M.  Gay-Lussac  and  my  own, 
being  1000  at  32°  F.,  becomes  1376  at  212°  F."  * 

1  See  pages  20-21. 

2  Note  by  Translator :— The  figure  0.3912,  as  given  by  Rudberg  and  by 
Magnus,  is  more  nearly  correct  than  0.392. 

8  See  page  22. 

4  Note  by  Translator: — If  Dalton  made  use  of  the  data  given  in  his 
memoir  of  1801  (See  p.  20-21)  as  a  basis  for  the  statement  quoted  by  Reg- 
nault  above — as  the  latter  evidently  assumes — he  was  clearly  in  error. 
It  happens  that  the  coefficient  in  accordance  with  which  a  volume  of 
1000  would  become  1325  through  a  rise  of  temperature  of  157°  F.,  or 
87.22°  C..— that  is,  for  the  number  of  degrees  lying  between  the  lowest 
temperature  he  employed,  55°  F.,  or  12.78°  C.,  and  the  boiling-point  of 
water— is  0.00207  for  each  Fahrenheit,  and  0.00373  for  each  Centigrade 
degree.  This  coincides  quite  closely  with  that  found  by  Gay-Lussac  in 
the  case  of  gases  when  the  volume  atO°  C.  is  compared  with  that  at  100° 
C.  Yet  it  is  clear  that  Dal  ton's  0.00373  represents  the  fraction  of  its 
volume  at  12.78°  C.  by  which  the  volume  of  a  gas  increases  for  each  de- 
gree between  12.78°  and  100  °C.;  while  Gay-Lussac' s  0.00375  represents 

72 


EXPANSION     OF    GASES 

Thus,  according  to  the  experiments  of  Rudberg,  the  coefficient 
of  expansion  of  air  accepted  for  a  long  time  by  physicists  is 
much  too  high.  Should  the  figure  0.3646,  which  is  the  mean 
result  of  his  experiments,  be  adopted  now  in  physical  compu- 
tations? 

It  seemed  to  me  that  new  experiments  were  called  for  to  re- 
move all  doubts  in  this  direction,  and  I  have  not  hesitated  to 
devote  myself  to  the  work,  feeling  that  the  determinations 
would  be  of  service  to  science,  even  if  they  merely  confirmed 
the  results  obtained  by  the  skillful  Swedish  physicist. 

I  have  carried  out  my  experiments  by  four  different  meth- 
ods. 

the  fraction  of  its  volume  at  0  °  C.  by  which  the  volume  of  a  gas  increases 
for  each  degree  between  0°  and  100°  C.  The  two  coefficients  are  not 
"  sensibly  the  same,"  because  they  do  not  represent  the  same  thing. 
The  words  in  quotation-marks  are  from  Preston's  Theory  of  Heat  (p.  190, 
footnote)  where  the  author,  following  Regnault,  assumes  that  Dal  ton  cal- 
culated his  coefficient  from  the  data  of  his  memoir  of  1801,  but  somehow 
misunderstands  Regnault' s  method  of  calculating  the  coefficient,  and 
claims  (incorrectly)  that  the  French  savant  had  overlooked  the  fact  that 
Dalton's  lowest  temperature  was  12.78°  C.  and  notO°.  Yet  if  we  use 
the  coefficient  0.003  <~3  in  the  way  Gay-Lussac  used  his  0.00375,  Dalton's 
1000  volumes  at  12.78°  would  have  been  reduced  to  954.5  at  0°,  and 
would  have  expanded  to  1312.4  at  100°,  instead  of  the  1325  which  he  re- 
cords. If,  on  the  other  hand,  we  make  use  of  the  coefficient  0.00392  cal- 
culated by  Regnault,  Dalton's  1000  volumes  at  12.78°  would  have  been 
reduced  to  952.3  at  0°,  and  would  have  expanded  to  325.6  at  100°, — 
which  is  what  actually  was  found. 

It  would  appear,  however,  that  neither  Rudberg,  Regnault  nor  Pres- 
ton has  carefully  read  Dalton's  statement  in  his  "  New  System,"  for  in 
it  he  says,  "  The  volume  at  32°  is  taken  1000,  and  at  212°  ,  1376,  accord- 
ing to  Gay-Lussac's  and  my  own  experiments.  As  for  the  expansion  at 
intermediate  degrees,  Gen.  Roy  makes  the  temperature  at  midway  of 
total  expansion,  116£  old  scale;  from  the  results  of  my  former  experi- 
ments (Manch.  Mem.  Yol.  5,  Part  2,  page  599)  the  temperature  may  be  es- 
timated at  119£;  but  I  had  not  then  an  opportunity  of  having  air  at  32  °. 
By  my  more  recent  experiments,  I  am  convinced  that  dry  air  at  32  ° 
will  expand  the  same  quantity  from  that  to  117°  or  118°  of  common 
scale,  as  from  the  last  term  to  212°,"  etc. 

A  study  of  this  passage  apparently  shows  that,  after  the  publication 
of  Gay-Lussac's  memoir,  Daltou  repeated  his  experiments  with  greater 
care,  using  the  freezing  point  of  water  as  his  lowest  temperature,  and 

F  73 


MEMOIKS    ON 

FIKST  SERIES  OF  EXPERIMENTS. 

The  determination  was  made  by  a  method  similar  to  that 
used  by  Kudberg  in  his  earlier  research,  and  which  is  in  other 
respects  that  by  the  aid  of  which  Dulong  and  Petit  made  the 
comparison  of  the  mercury  thermometer  with  the  air  thermom- 
eter. I  replaced  Rud berg's  small  bulb,  however,  which  held 
but  150  to  200  grams  of  mercury,  by  cylindrical  reservoirs  of  25 
to  30  mm.  diameter  and  of  about  110  mm.  length,  capable  of 
holding  800  to  1000  grams  of  mercury.  I  preferred  the  cylin- 
drical to  the  spherical  form,  because  the  former  does  not  pro- 
duce the  refraction  effects  of  the  latter,  which  are  likely  to  in- 
troduce considerable  errors  when  the  heights  of  the  mercury 
[columns]  drawn  up  are  read  from  a  distance  with  the  aid  of  a 
glass.  It  also  seemed  advisable  to  me  to  increase  the  capacity 
of  the  air  reservoir. 

The  cylindrical  reservoir  AB  (Fig.  4)  ended  in  a  capillary 
tube  A  CD  the  bore  of  which  varied  in  different  cases  between 
£  mm.  and  2  mm.  The  capillary  tube  was  drawn  out  to  a  point 
and  its  end  was  bent  at  a  right  angle. 

This  apparatus  was  fixed  by  means  of  a  cork  E  in  the  cover 

obtaining  results  confirming  closely  those  of  his  French  contemporary. 
These  later  figures  are  thus  the  ones  referred  to  in  the  first  part  of  the 
passage  quoted  above.  The  fact  that  l<  more  recent  experiments"  with 
"dry  air  at  32°  "  were  made  by  Dalton  seems  to  have  been  entirely 
overlooked  by  the  authors  referred  to  above. 

Moreover,  nowhere  in  his  1801  memoir  does  Dalton  calculate  the  coef- 
ficient of  expansion  between  0°  and  100°  of  the  gases  with  which  he 
experimented.  He  does  not  appear  to  have  considered  the  question  of 
their  volume  at  32°  F.  at  all  ;  his  whole  attention  was  directed  to  their 
behavior  above  55°  F.  Yet  Biot,  in  his  Treatise  on  Physics,  praises 
Dalton' s  skill  as  an  experimenter  and  states  that  the  latter  found 
the  expansion  of  gases  between  0°  and  100  °  to  be  0.372.  (See  page  59.) 
Biot  must  himself  have  calculated  the  figure  0.372  from  Dalton's  data 
of  1801 — for  Dalton  does  not  give  it  in  either  of  the  extracts  quoted 
above, — or  else  it  is  based  upon  later  and  more  accurate  determinations 
made  by  the  English  philosopher  after  the  publication  of  the  work  of 
Gay-Lussac. 

It  seems  much  more  reasonable  to  suppose  that  Dalton  actually  ob- 
tained results  — after  1801 — justifying  the  claim  he  makes  in  his  New 
System  and  explaining  the  statement  of  Biot,  than  to  suppose  that  both 
Dalton  and  Biot  were  guilty  of  the  same  arithmetical  blunder. 

74 


EXPANSION     OF     GASES 

KK'  of  a  tin-plate  vessel  V  in  which  water  is  boiled.  The  va- 
por which  is  formed  in  the  lower  part  of  the  vessel  is  obliged 
to  pass  out  by  way  of  the  annular  space  LL'  which  is  for  the 
purpose  of  preventing  its  cooling  by  reason  of  the  contact  of 
the  outside  air,  before  escaping  by  the  lateral  pipe  M.  At  N 
there  is  a  small  tubulure  and,  in  the  inner  wall  and  directly  oppo- 
site, a  small  round  hole  0.  In  the  neck  is  fitted  by  means  of  a 
cork  a  bent  glass  tube  F  which  acts  as  a  manometer,  and  one 
of  the  open  ends  of  which  passes  through  the  hole  0  and  is 
thus  in  direct  communication  with  the  interior  of  the  vessel  V. 
The  other  end  is  open  to  the  air.  The  water  column  contained 


FIG.  4. 


in  the  two  vertical  arms  shows,  by  the  difference  of  level, 
whether  the  pressure  is  the  same  inside  and  out.  The  reser- 
voir AB  and  the  capillary  tube  attached  to  it  are  thus  com- 
pletely surrounded  by  the  vapor  of  boiling  water. 

When  the  water  is  boiling  vigorously,  the  tip  of  the  capillary 
tube  is  connected  by  means  of  a  rubber  tube  with  a  drying 
apparatus.  This  consists  of  U-shaped  tubes  G,  G'}  each  about 

75 


MEMOIKS     ON 


a  meter  long  and  20  mm.  in  diameter.  These  tubes  are  filled 
with  broken  pumice  stone  moistened  with  concentrated  sulphu- 
ric acid  ;  they  are  connected  with  one  another  by  rubber  tubes, 
and  with  a  small  hand  pump  P.  By  means  of  this  pump  a 
vacuum  is  produced  twenty-five  or  thirty  times  in  the  appara- 
tus, and,  eacli  time,  the  air  is  allowed  to  enter  again  very 
slowly  by  opening  the  taps  in  the  proper  way.  The  taps  are 
left  wide  open  the  last  time  so  that  the  air  in  the  reservoir  is  in 
direct  communication  with  the  atmosphere. 

The  apparatus  is  left  in  this  condition  for  from  a  half-hour 
to  an  hour  ;  the  drying  apparatus  is  then  disconnected.     As  it 

is  conceivable  that  the 
pumice  stone  might  by 
chance  become  packed 
somewhere  in  the  tubes  GG' 
and  the  enclosed  acid  pro- 
duce a  continual  obstruc- 
tion to  the  entrance  of  the 
air,  and  as  in  consequence 
an  excess  of  pressure  would 
be  needed  to  force  it  into 
the  reservoir,  I  have  always 
taken  care  to  disconnect 
first  the  rubber  tube  a; 
it  is  evident  that  in  this 
way,  even  if  the  air  of  the 
reservoir  is  under  a  slightly 
lower  pressure  than  that 
of  the  atmosphere,  it  will 
still  be  dried  air,  that  con- 
tained between  a  and  D, 
which  will  enter  the  res- 
ervoir and  produce  equilib- 
rium. In  my  experiments 
this  precaution  was  unneces- 
sary, as  the  pumice  stone  was  only  soaked  in  sulphuric  acid. 
The  rubber  tube  D  is  then  removed  and  the  apparatus  allowed 
to  stand  several  minutes  in  direct  communication  with  the 
atmosphere  ;  finally  the  drawn-out  tip  of  the  capillary  tube  is 

76 


FIG.  5. 


EXPANSION     OF     GASES 


closed  by  means  of  a  blowpipe,  and  at  the  same  time  the  height 
of  the  barometer  is  recorded.  We  thus  have  the  reservoir  AB 
filled  with  dry  air  at  the  temperature  of  the  [water-]  vapor  and 
under  the  pressure  of  the  atmosphere. 

The  reservoir  after  being  removed  from  the  heater  was 
fastened  in  the  support  shown  in  perspective  in  Fig.  5.  This 
support  consists  of  a  circular  plate  EE'  in  the  centre  of  which 
is  a  short  tube  0,  and  supported  upon  three  vertical  legs  P,  P', 
P",  joined  for  greater  steadiness  at  their  lower  ends  by  a  circle 
of  metal  QQ'.  Three  inclined  metal  rods  are  arranged  sym- 
metrically about  the  short  tube  0;  they  terminate  above  in 
small  balls  with  screw  adjustment.  The  air  reservoir  AB  rests 
upon  these  balls  and  the  capillary  stem  is  held  by  a  cork  fitted 
into  the  short  tube.  Greater  steadiness  is  given  it  by  means  of 
the  screw  V  working  in  the  movable  cross-bar  MN. 

Upon  one  of  the  vertical  legs  P'  is  mounted  a  cross-bar  mn 
which  carries  a  movable  piece  shown  on  a 
larger  scale  in  Fig.  6.  It  consists  of  a  little 
iron  spoon  JT  attached  to  an  iron  stem  fg 
which  can  be  raised  or  lowered  at  will  in  the 
piece  abed.  This  piece  can  be  slid  along 
the  horizontal  ami  mn,  which  in  turn  can 
be  fastened  at  any  height  to  the  leg  P'  by 
means  of  the  set  screw  v. 

Upon  another  leg  P  is  arranged  a  horizon- 
tal arm  st  which  is  capable  of  adjustment 
and  can  be  held  by  a  set  screw;  it  carries  a 
screw  rod  ending  at  top  and  bottom  in  a 
rounded  point. 

The  reservoir  is  fixed  in  the  apparatus  in  such  a  way  that  the 
bent  portion  CD  of  the  capillary  tube  is  pointed  directly 
towards  the  leg  P',  and  a  mark  is  made  upon  the  leg  P>  at  the 
height  at  which  the  adjustable  piece  mn  must  be  fastened  in 
order  that  the  centre  of  the  little  spoon  K  shall  be  exactly  at 
the  height  and  in  the  direction  of  the  bent  portion  of  CD. 

This  being  arranged,  the  apparatus  is  placed  above  a  small 
bath  of  mercury,  in  such  a  way  that  the  capillary  tube  dips  in 
the  mercury  at  least  5-6  centimeters.  A  very  fine  file  mark 
has  been  previously  made  across  the  stem  CD  at  the  point 

77 


FIG.  6. 


MEMOIRS    ON 

where  it  is  desired  to  break  it  off.  The  tip  is  then  broken  off 
with  a  small  pair  of  pincers;  the  mercury  enters  the  capillary 
tube  and  rises  to  a  certain  height  in  the  reservoir;  this  is  then 
surrounded  with  snow  or  finely  crushed  ice,  and  the  apparatus 
is  allowed  to  stand  undisturbed  for  at  least  an  hour  or  an  hour 
and  a  half,  in  order  to  let  it  come  exactly  to  the  temperature  of 
melting  ice.  Meantime  the  spoon  has  been  carefully  lowered 
to  the  proper  depth  in  the  mercury.  From  time  to  time  the 
apparatus  is  gently  jarred  to  overcome  the  resistance — should 
there  be  any — which  the  mercury  might  meet  with  in  its  ascent 
within  the  capillary  tube. 

The  little  spoon  is  then  pushed  forward  along  its  arm  until 
the  opening  of  the  capillary  tube  is  buried  in  the  wax,  and  at 
the  same  time  the  exact  height  of  the  barometer  is  recorded. 
The  arm  st  is  lowered  along  the  leg  P,  and  the  point  of  the 
screw  is  accurately  adjusted  to  the  level  of  the  mercury  surface 
in  the  bath.  The  ice  which  enveloped  the  tube  is  completely 
removed,  and  the  drawn-up  column  of  mercury  is  allowed  to 
come  to  the  temperature  of  the  surrounding  air. 

It  now  remains  to  measure  the  height  of  the  drawn-up  mer- 
cury ;  for  this,  I  made  use  of  a  cathetometer  of  M.  Gambey's 
design,  which  gives  directly,  with  its  vernier,  a  reading  within 
a  fiftieth  of  a  millimeter.  One  sights  with  the  horizontal  tele- 
scope at  the  level  of  the  mercury1  in  the  tube  AB,  then  the 
glass  is  lowered  and  is  sighted  at  the  upper  point  of  the  screw; 
adding  to  the  difference  of  level  thus  found  the  distance  be- 
tween the  two  points  of  the  screw — which  has  been  previously 
measured  with  the  same  instrument — one  has  the  total  height 
of  the  drawn-up  mercury.  More  commonly  we  sight  directly 
at  the  lower  point  of  the  screw,  after  having  lowered  the  bath 
T — which  is  easily  done  by  removing  the  support  8. 

The  reservoir  AB  with  the  mercury  drawn  up  is  then  re- 
moved. It  is  weighed,  then  completely  filled  with  mercury 


1  Care  must  be  taken,  when  one  sights  with  the  glass  at  the  upper 
line  of  the  meniscus,  not  to  be  led  into  error  through  reflection-phe- 
nomena at  the  curved  surface  of  the  mercury.  The  procedure  which 
seems  to  me  surest,  consists  in  placing  a  candle  in  the  line  of  the  menis- 
cus and  behind  it,  in  such  a  way  that  the  shape  of  the  meniscus  is  out- 
lined in  black  against  the  flame  of  the  candle. 

78 


EXPANSION     OF    GASES 

which  is  thoroughly  boiled  to  drive  out  air  and  moisture  en- 
tirely; finally  it  is  buried  in  ice  while  the  open  end  dips  in  a 
dish  full  of  mercury.  After  an  hour  and  a  half  or  two  hours, 
when  one  is  certain  that  the  mercury  is  perfectly  stationary  at 
the  opening  in  the  tip,  the  ice  is  removed  and  the  mercury 
which  flows  out  of  the  apparatus  through  expansion  is  caught 
in  a  small  capsule.  The  reservoir  is  next  hung  in  the  same 
boiler  which  was  used  to  expand  the  air  ;  the  mercury  which 
escapes  is  caught  in  the  little  capsule.  The  barometer  is  read 
while  the  boiling  is  in  progress.  The  mercury  caught  in  the 
capsule  is  weighed,  as  well  as  the  reservoir  with  the  mercury 
it  still  contains.  The  weight  of  the  mercury  at  0°  which 
exactly  fills  the  reservoir  at  0°  is  consequently  known,  and 
one  has  given  all  that  is  necessary  for  calculating  (1)  the  expan- 
sion of  the  containing  vessel;  (2)  the  expansion  of  the  air  con- 
tained. 

Let  H  be  the  barometric  pressure  at  the  time  when  the 
drawn-out  tip  of  the  tube  was  sealed  with  the  blowpipe ; 

TtliQ  boiling  point  of  water  under  this  pressure; 

ff"  the  barometric  pressure  when  the  tip  was  closed  with  the 
wax  under  the  mercury  ; 

h  the  height  of  the  drawn-up  mercury  ; 

P  the  weight  of  the  mercury  drawn  up  ; 

P'  the  weight  of  the  mercury  at  0°  which  fills  the  apparatus 
at  0°; 

p  the  weight  of  the  mercury  forced  out  by  expansion  between 
the  temperature  of  melting  ice  and  that  (Ti)  of  water  boiling 
under  a  barometric  pressure  H\ ; 

100  6  the  amount,  finally,  by  which  a  volume  1  of  glass  ex- 
pands between  0°  and  100°; 

And  100  a  the  amount  by  which  a  volume  1  of  dry  air  expands 
between  the  same  limits. 

The  heights  H,  H',  h,  are  supposed,  for  greater  simplicity, 
to  have  been  reduced  to  0°  by  calculation.  We  shall  have  for 
determining  3  the  equation: 


MEMOIKS    ON 
whence 


(P'-p)      l+_±- 
5550  J 


PT 

and  for  calculating  a, 


(P/  -  P)  (1  +  a  T)  ~  =  P'  (1  +  6  T), 


whence 


In  making  my  experiments  in  the  way  that  has  been  de- 
scribed I  have  not  been  slow  to  see  a  very  serious  source  of 
error.  In  breaking  off  the  point  of  the  capillary  tube  under 
the  mercury,  I  noticed  that  even  when  the  stem  dipped  almost 
a  decimeter  into  the  mercury,  there  was  always  a  minute  quan- 
tity of  air  drawn  in  which  added  itself  to  the  air  in  the  reser- 
voir. The  mercury  does  not  wet  the  glass,  and  there  is  a  little 
space,  probably  filled  with  air,  between  the  glass  tube  and  the 
mercury.  It  is  by  way  of  this  sheath  that  the  outside  air  is 
drawn  in,  by  a  process  similar  to  that  of  a  bugle,  during  the 
ascending  movement  of  the  mercury.  This  phenomenon  of 
aspiration  is  sometimes  noticed  by  the  fact  that  whole  bubbles 
of  air  rise  in  the  capillary  tube  after  the  manner  of  a  piston. 

I  had  much  difficulty  at  first  in  preventing  this  result.  By 
placing  upon  the  part  of  the  tube  under  the  mercury  many 
small  discs  of  a  substance  wetted  by  mercury,  like  well  cleaned 
brass,  I  succeeded  in  preventing  the  entrance  of  the  outside  air. 
In  order  to  be  completely  out  of  reach  of  this  source  of  error, 
I  combined  this  method  with  another  which  consists  in  pour- 
ing upon  the  mercury,  before  breaking  off  the  point  and  after 
having  taken  hold  of  the  tip  with  the  pincers,  a  layer  of  con- 
centrated sulphuric  acid.  This  layer  of  acid  is  removed  when 
the  reservoir  has  been  lowered  to  0°  by  the  ice  ;  the  surface  of 
the  bath  of  mercury  is  cleaned  and  then  the  arm  Kn  is  lowered. 

It  is  also  important  that  the  iron  pincers  with  which  the 
point  of  the  capillary  tube  is  broken  off,  should  always  be  at 
some  distance  from  the  scratch  of  the  file  upon  the  stem  by 
which  the  break  is  brought  about.  Otherwise,  if  the  opening 
of  the  capillary  tube  touches  the  pincers,  one  may  see  rise  in 

80 


EXPANSION    OF    GASES 

the  tube  a  little  bubble  of  air  which  has  its  source  in  that  which 
remains  adhering  to  the  surface  of  the  pincers. 

I  bring  together  in  the  following  table  the  results  obtained 
in  the  fourteen  experiments  I  made  by  this  method. 


Number 
of 
Experi- 
ment 

II 

, 

h 

P 

ff 

T 

Hi 

ft 

P 

1005 

1+100  a 

ram. 

mm. 

mm. 

gr. 

gr. 

0 

mm. 

0 

gr. 

1 

760.03 

760.57 

111.02 

856.145 

119.915 

100.00 

760.60 

100.02 

12.870 

0.002714 

1.36556 

2 

759.67 

755.72 

98.67 

770.465 

116.780 

99.99 

753.75 

99.7V 

11.665 

0.002576 

1.36626 

3 

750.40 

749.81 

99.82 

805.75 

12260 

99.64 

" 

•' 

" 

0.002650 

1.36659 

4 

744.61 

744.78 

100.60 

800.27 

120.19 

99.43 

744.60 

99.43 

12.050 

0.002601 

1.36579 

5 

747.99 

748.79 

106.35 

790.69 

114.31 

99.55 

748.20 

99.56 

11.931 

0002592 

1.36625 

6 

751.48 

752.68 

102  32 

913.48 

137.74 

99.68 

" 

11 

" 

0.002680 

1  .36549 

7 

763.27 

763.27 

97.45 

855.24 

136318 

100.13 

763.30 

100.13 

13.015 

0.002544 

1.36673 

8 

765.34 

765.00 

102.50 

854.86 

130.60 

100.20 

765.30 

100.20 

13  025 

0.002537 

1.36634 

9 

764.14 

763.92 

102.87 

805.14 

122.79 

100.16 

764.10 

100.16 

12.225 

0.002583 

1.36689 

10 

763.34 

763.62 

102.17 

854.79 

131.10 

100.13 

763.51 

100.14 

13.005 

0.002548 

1.36610 

11 

754.55 

752.34 

105.80 

790.49 

113.364 

99.80 

754.50 

99.80 

11.942 

0.002607 

1.36671 

12 

750.29 

750.57 

68.48 

853.82 

163.794 

99.64 

" 

M 

" 

0.002570 

1.36591 

13 

751.94 

751.72 

74.91 

769.452 

141.710 

99.70 

750.86 

99.66 

11.633 

0.002576 

1.36041 

14 

764.62 

764.50 

122.31 

853.447 

108.417 

100.18 

768.63 

100.32 

13.008 

0.002551 

1.36673 

19.12776 

Mean      •     ^  .     =  1.36623 

Extremes. 

..    Ji- 

56689 
!6549 

ll.! 

Greatest  difference  0.00140 

The  mean  for  the  fourteen  experiments  is  1.36623.  The 

difference  between  the  two  extreme  figures 1.36689 

and 1.36549 

is .0.00140 

that  is,  what  amounts  to,  at  most,  TT5V^  of  the  quantity  to  be 
measured. 

The  figures  given  by  the  fourteen  experiments  are  all  much 
higher  than  the  mean  1.3646  which  Rudberg  obtained  in  the 
experiments  made  by  a  quite  similar  method.  I  believe  that 
this  difference  can  be  ascribed  to  the  fact  of  the  sucking  in,  in 
Rudberg's  experiments,  of  the  outside  air  ;  it  seems  unlikely 
that,  working  by  his  method,  this  source  of  error  could  have 
been  avoided  :  on  the  other  hand  it  is  clear  that  it  escaped  his 
notice,  if  only  because  he  does  not  mention  it. 

The  errors  introduced  through  this  sucking-in  are  so  much 
the  more  noticeable  as  one  works  with  a  smaller  volume  of  air. 

I  did  not  at  first  succeed  in  preventing  this  sucking-in  ;  I  am 

81 


MEMOIRS     ON 

convinced  that  in  my  earlier  experiments  it  still  had  a  notice- 
able effect  and  rendered  some  of  my  figures  too  low.  What  con- 
firms me  in  this  view  is  that,  starting  from  the  time  when  the 
sucking-in  was, made  impossible,  I  obtained  no  figure  lower 
than  1.3658. 

SECOND  SERIES  OF  EXPERIMENTS. 

The  experiments  of  this  second  series  were  made  by  a  method 
slightly  different  from  that  followed  in  the  former  series  ;  but 
the  apparatus  was  arranged  so  that  the  volume  of  air  subjected 
to  experiment  remained  practically  the  same  at  the  temperature 
of  melting  ice  and  at  that  of  boiling  water,  so  that  the  whole 
effect  of  the  expansion  by  heat  is  changed  to  a  variation  of 
tension. 

A  glass  bulb  of  350  to  400  cubic  centimeters'  capacity  is 
sealed  to  a  capillary  tube  about  38  centimeters  long  ;  on  this 
capillary  tube,  at  a  distance  of  11  centimeters  from  the  bulb, 
is  put  a  piece  of  very  regular  tubing  about  50  mm.  long  and  of 
sufficiently  great  diameter  to  show  only  a  very  slight  capillary 
effect.  The  capillary  tube  at  its  end  is  drawn  out  to  a  point 
and  bent  at  a  right  angle. 

The  first  thing  to  be  done  consists  in  calibrating  this  appara- 
tus accurately  and  determining  its  coefficient  of  expansion. 
For  this  it  must  be  completely  filled  with  mercury  at  the 
temperature  of  0°.  This  is  a  delicate  operation,  as  all  physi- 
cists will  agree,  for  it  is  nothing  else  than  constructing  a 
thermometer  whose  reservoir  shall  contain  about  5  kilograms 
of  mercury. 

To  introduce  the  mercury,  the  bulb  is  connected,  by  means 
of  a  rubber  tube  D,  Fig.  7,  with  a  bent  tube  DE  fastened  to  a 
support  ;  mercury  is  poured  into  this  tube  DE.  If  the  bore 
of  the  capillary  tube  is  not  very  small,  the  bulb  is  easily  filled 
three-quarters  full  without  any  necessity  for  exhausting  through 
the  tube  E ;  but  to  succeed  in  filling  it,  one  may  have  to 
exhaust  several  times  by  means  of  the  tube  E.  The  best  way 
is  to  connect  this  tube  with  the  small  pump  of  Fig.  4,  page  75. 
The  bulb  may  thus  be  filled  in  a  very  short  time. 

It  is  then  necessary  to  bring  the  mercury  to  boiling  :  to  this 


EXPANSION     OF    GASES 

end  the  bulb  A  is  placed  upon  a  hollow  grating  GG  over  a 
small  furnace  F,  Fig.  8,  the  capillary  tube  having  an  inclina- 
tion of  about  45  °  and  its  bent  end  CD  being  below  the  surface 
in  a  dish  full  of  very  pure  mercury.  Some  coals  are  then  put 
in  the  furnace,  below  the  grating,  then  they  are  successively 
placed  upon  the  grating  itself  and  upon  the  bulb,  and  finally 


FIG.  7. 


FIG.  8. 


the  latter  is  entirely  covered  with  hot  coals.  When  the  mercury 
in  the  bulb  approaches  the  boiling  temperature,  the  mercury  in 
the  dish  D  is  heated  with  an  alcohol  lamp,  and  with  a  second 
alcohol  lamp  the  capillary  tube  is  cautiously  heated  throughout 
its  length.  As  soon  as  the  mercury  begins  to  boil  in  the  bulb, 
the  operation  must  be  watched  with  the  greatest  care  ;  for  if  this 
boiling  becomes  too  vigorous,  if  it  drives  out  of  the  bulb  too 
large  a  volume  of  liquid  mercury  displaced  by  mercury  vapor, 
it  is  almost  impossible  to  prevent  the  apparatus  being  broken 
at  the  instant  when,  the  boiling  having  stopped,  the  mercury 
rushes  back  into  the  bulb  ;  this  results  in  very  violent  hammer- 
ing and  return-shocks  which  ordinarily  extend  as  far  as  the 
bent  part  CD  of  the  capillary  tube. 

Therefore  as  one  sees  the  mercury  boiling  in  the  vessel,  a 
part  of  the  coals  must  quickly  be  removed  and  the  operation 
be  made  as  smooth  as  possible.  The  coals  are  taken  away 
entirely  as  soon  as  the  moisture  seems  to  have  been  completely 

83 


ME  MO  IKS     ON 

driven  out,  or  even  when  the  volume  of  mercury  vapor  has 
become  considerable.  The  mercury  then  returns  into  the 
apparatus  and,  as  it  has  been  previously  heated  in  the  dish,  it 
does  not  break  the  capillary  tube,  as  it  would  certainly  do  with- 
out this.  When  the  bulb  is  once  more  full,  one  looks  to  see  if 
a  trace  of  moisture  remains  ;  in  case  some  still  remains,  the 
boiling  must  be  begun  again.  Speaking  generally,  it  serves 
better  to  bring  it  to  the  boiling  point  again  and  again,  rather 
than  to  continue  the  boiling  for  too  long  a  time  ;  in  this  way 
the  breaking  of  the  apparatus  is  more  easily  avoided. 

When  the  vessel  is  completely  full  of  mercury,  it  is  allowed 
to  cool  to  the  temperature  of  the  air,  then  is  surrounded  with 
a  thick  envelope  of  crushed  ice.  It  requires*  many,  hours  for 
the  mass  of  mercury  to  arrive  absolutely  at  the  temperature  of 
0°.  When  it  is  certain  that  this  point  has  been  reached,  the 
dish  full  of  mercury  is  removed  and  is  replaced  by  a  small 
empty  capsule.  The  ice  having  been  got  out  of  the  way,  the  bulb 
is  warmed  with  the  aid  of  hot  coals  placed  at  some  distance 
from  it,  so  as  to  raise  it  to  a  temperature  some  degrees  higher 
than  the  surrounding  one;  then  it  is  hung  in  a  small  bag  in 
the  boiling  apparatus  of  Fig.  4  [page  75],  to  which  an  exten- 
sion has  been  fitted,  so  that  the  whole  capillary  tube  is  sur- 
rounded by  the  steam,  and  the  mercury  is  caught  in  the  same 
capsule.  By  weighing  the  mercury  forced  out  and  that  re- 
maining in  the  apparatus,  it  is  evident  we  have  the  necessary 
data  for  calculating  the  volume  of  the  apparatus  at  0°  and 
the  extent  to  which  it  expands  between  0  and  100°. 

To  find  the  expansion  of  air,  the  bulb  is  hung  in  the  boiler 
after  the  mercury  has  been  so  completely  removed  that  not  the 
smallest  globule  remains  upon  the  walls  or  in  the  tube.  The 
bulb  is  connected  with  the  drying  apparatus,  Fig.  4.  In  a 
word,  one  goes  to  work  exactly  as  has  been  described  in  the 
account  of  the  former  series. 

When  the  end  of  the  capillary  tube  has  been  sealed  with  a 
lamp,  the  apparatus  is  adjusted  to  a  support  shown  in  Fig.  9. 
The  expanded  part  B  of  the  tube  comes  below  the  plate  EE' '. 
By  means  of  a  cork  on  the  stem  at  M,  a  tin-plate  tray  is  put  in 
place,  in  which  crushed  ice  must  be  piled  up,  to  keep  the  vol- 
ume B  at  0°.  The  capillary  tube  dips  in  a  small  bath  of  mer- 

84 


EXPANSION    OF    GASES 

cury  T.  The  tip  of  the  bent  part  CD  is  broken  off,  all  the 
precautions  being  exactly  followed  which  have  been  pointed 
out  in  the  first  account,  to  prevent  the  entrance  of  air;  finally 
the  vessel  A  is  surrounded  with  ice  after  having  put  over  it 
from  above  a  cylinder  of  tin-plate  which  is  entirely  filled  with 
crushed  ice.  In  the  same  way  the  volume  B  and  the  part  of 
the  capillary  stem  which  is  above  the  tray  M  are  surrounded 
with  ice. 

Upon  one  of  the  legs  of  the  support  P  is  arranged  a  mov- 
able arm  mn  carrying  the  small  adjustable  spoon  of  Fig.  6; 
this  is  lowered  into  the  mercury.  A  mark  has  previously  been 


FIG.  9. 

made  upon  the  leg  P'  at  the  point  where  mn  should  be  clamped 
in  order  that  the  spoon  JTmay  be  at  the  level  and  in  a  line 
with  the  tube  CD. 

The  apparatus  having  been  left  in  the  ice  for  about  an  hour, 
the  tip  D  is  sealed  by  pushing  forward  the  spoon  K,  and  at  the 
same  time  the  barometer  is  read;  finally,  the  point  of  the 
screw  #,  which  is  arranged  upon  a  small  special  apparatus  E, 
is  made  to  coincide  with  the  surface  of  the  mercury  in  the 
bath. 

The  ice  which  is  in  the  tray  M  is  then  removed.  At  the 
end  of  three-quarters  of  an  hour  or  an  hour,  when  it  is  certain 
that  the  column  of  mercury  drawn  up  is  in  temperature-equi- 

85 


MEMOIRS     ON 

librium  with  the  surrounding  air,  the  height  of  this  column  is 
measured  with  the  cathetometer.  The  dimensions  of  the  tube 
and  the  level  at  which  the  mercury  bath  is  placed,  are  such  that 
the  mercury  comes  to  rest  in  the  space  B  and  fills  it  about 
half  full. 

The  apparatus  is  detached  and  the  mercury  which  has  made 
its  way  in  is  weighed. 

The  tubing  of  which  the  space  B  is  made  was  chosen  in  suc- 
cessive cases  of  different  diameters;  these  dimensions  were 
never  great  enough  for  the  capillarity  to  become  nil,  but  the 
capillary  depression  is  determined  each  time,  by  direct  experi- 
ment, in  that  part  of  the  tube  where  the  surface  of  the  mer- 
cury comes  to  rest.  For  this  purpose  this  tube  is  held  vertical 
with  both  ends  open,  and  dipping  in  a  bath  of  mercury.  On 
the  slide  which  supports  the  glass  of  the  cathetometer  a  hori- 
zontal metallic  rod  is  fastened,  to  the  end  of  which  is  fixed  a 
vertical  pointer  whose  tip  is  adjusted  for  contact,  successively 
with  the  top  of  the  meniscus  in  the  tube  and  with  the  mercury 
surface  in  the  bath.  The  distance  traversed  by  the  zero  of 
the  vernier  of  the  instrument  is  the  capillary  depression. 

We  then  have  all  the  data  necessary  for  calculating  the  ex- 
pansion of  the  air.  Using  the  same  letters  to  designate  simi- 
lar things,  as  in  the  former  method  and,  in  addition,  repre- 
senting by  c  the  capillary  depression  in  the  space  B,  clearly  we 
have  the  equation 

(1  +  6  T)  H  =  (i  —  ^VH'  —  (h  +  c)]  (1  +  &  T)\ 
whence 

l  +  aT  =     \H'-(h  +  c)}     /VIH 


Let  us  assume  in  all  cases  that  the  columns  of  mercury  have 
been  reduced  to  0  °  by  calculation. 

Three  different  vessels,  A,  B,  C,  were  used  in  these  experi- 
ments; to  these  were  successively  joined  capillary  tubes  of 
different  bores. 

I  shall  distinguish  as  many  series  of  experiments  as  different 
forms  of  apparatus. 

86 


EXPANSION    OF    GASES 


I.  The  results  with  this  apparatus  are  as  follows: 

p  =  4330.0  gr. 
c  =        1.10  mm. 

The  coefficient  of  expansion  of  the  glass  could  not  be  deter- 
mined as  the  apparatus  was  broken  during  the  boiling  of  the 
mercury.  For  this  one  experiment  made  with  vessel  A  the  as- 
sumption is  made  that  100<5  =  0.002306,  as  was  found  by  ex- 
periment with  the  vessel  B. 

The  experiment  upon  the  expansion  of  air  gave 

.  4- 100  a 

1.36629 

II.  This  apparatus  was  made  with  the  vessel  B;  we  have: 

p=4274.34gr., 
p  =     65.708, 
c=        1.10mm., 
//  =    749.37,        whence  Tl  =  99.60° . 

We  deduce  from  this 

100^  =  0.002306. 


H 

H' 

h  -f-  c 

P' 

T 

mm. 
739.61 

mm. 

739.86 

mm. 
194.38 

gr. 
14,233 

99.23 

H 

H' 

2 
3 

mm. 
739.24 
758.64 

mm. 
739.21 
758.53 

mm. 

193.58 
199.51 


P' 

gr. 

17,735 
17,335 


T      |14-100a 


99.22° 
99.95 


1.36645 
1.36593 


III.  Apparatus  made  with  the  vessel  B,  but  using  for  the 
space  B  on  the  capillary  tube,  a  tubing  of  much  greater  diame- 
ter. 

For  this  apparatus  it  was  found 
P  =4306. 86  gr., 
p   =     66.68, 
c   =       0.22  mm., 
Hi=  769.04,  hence  T\  =  100.34    ; 
from  which  we  find 

100  6  =  0.002302. 
With  this  apparatus  I  obtained  the  following  figures  : 


H 

H' 

h  +  c 

P' 

T 

1  +  100  a 

mm. 

mm. 

mm. 

gr. 

4 

764.70 

764.31 

198.78 

36.095 

100.18° 

1  .36610 

5 

767.24 

767.19 

199.98 

34.825 

100.27 

1.36585 

6 

768.10 

767.40 

199.62 

34.845 

100.30 

1.36590 

7 

770.57 

770.70 

200.86 

34.490 

100.40 

1.36615 

8 

771.07 

770.26 

199.53 

41.780 

100.41 

1.36691 

87 


MEMOIRS     ON 

IV.  Apparatus  made  with  the  vessel  C. 
P  =  4878.60  gr., 


P  = 
c   = 
Hi  = 
From  this  we  deduce 


74.795, 

0.54  mm., 

749.32,  hence  Ti  =  99.60°. 
100  6  =  0.002349. 


II 

JET 

h  +  c 

P' 

T 

1  +  100  a 

mm. 

mm. 

mm. 

gr. 

9 

748.13 

745.89 

193.04 

32.42 

99.56° 

1.36708 

10 

754.10 

751.51 

194.73 

30.64 

99.78 

1.36695 

11 

740.14 

744.53 

196.86 

32.305 

99.26 

1.36633 

12 

746.91 

748.  13 

196.23 

31.355 

99.51 

1.36708 

13 

747.54 

747.28 

194.69 

31.486 

99.53 

1.36650 

V.  Apparatus  made  with  the  bulb  C,  but  using  for  the  space 
B  a  tubing  of  a  greater  diameter  and  for  capillary  tubing  one 
of  finer  bore. 

For  this  apparatus  we  have  : 

P  =  4923.60gr., 
c   =        0.22  mm.  ; 
we  have  assumed  100  6  =  0.002349. 


H 

H' 

h  +  c 

P' 

T 

1  +100  a 

mm. 

mm. 

mm. 

gr. 

14 

746.69 

747.16 

191.98 

58.551 

99.50° 

1.36615 

15 

751.97 

750.18 

191.50 

56.69 

99.70 

1.36594 

16 

746.49 

746.19 

191.76 

54.865 

99.50 

1.36660 

17 

752.50 

751.45 

192.17 

61.30 

99.72 

1.36666 

VI.  Apparatus  constructed  with  the  same  bulb,  substituting 
for  the  finer  capillary  tube  another  of  a  larger  bore. 
The  data  for  this  apparatus  are  the  following  : 
P  =  4926.4  gr., 
c  =        0.22  mm. ; 
we  have  assumed  100  6  =        0.002349. 

This  apparatus  was  used  for  but  one  experiment  upon  atmos- 
pheric air ;  it  was  intended  for  some  experiments  upon  other 


18 


H 
mm. 

758.24 


H' 

mm. 

758.78 


mm. 
195.68 


P 

gr. 

58.31 


T 

99.93 


1  +  100  a 
1.36614 


Then  bringing  together  all  the  figures  obtained  in  this  series 
of  experiments — 


88 


EXPANSION    OF    GASES 


1.36629 
1.36645 
1.36593 
1.36610 
1.36585 
1.36590 
1.36615 
1.36591 
1.36708 


1.36695 
1.36633 
1.36708 
1.36650 
1.36615 
1.36594 
1.36660 
1.36666 
1.36614 


The  mean  of  all  these  experiments  is 

1.36633. 

It  does  not  practically  differ  from  that  obtained  in  the  former 
series. 

THIRD  SERIES  OF  EXPERIMENTS. 

This  third  series  of  experiments  was  made  by  means  of  an  ap- 
]of  o 


paratns  copied  from  that  described  by  Rudberg  in  his  second 
memoir  and  which  is  represented  in  Fig.  3  [page  70  ].     The  ap- 
paratus which  I  constructed  is  shown  in  Figs.  10,  11,  12. 
G  89 


MEMOIES    ON 

A  cylindrical  glass  reservoir  AB,  35  millimeters  in  diameter 
and  170  mm.  long,  is  sealed  to  a  capillary  tube  BCDE,  twice 
bent  at  right  angles.  This  tube  terminates  in  a  piece  of  tubing 
EE  of  much  larger  size,  which  dips  iu  a  small  mercury  bath 
MM'. 

This  bath  consists  of  a  cylinder  of  heavy  glass  whose  two 
edges  are  tightly  pressed  against  the  two  cast  mountings  M, 
M',  by  means  of  the  screw  rods  t,  t ',  t".  The  upper  casting  has 
two  tubulures  T,  T',  provided  with  screw  threads  on  the  outside. 
These  tubulures  are  closed  by  two  copper  screw  caps  bored 
through  the  centre  with  holes  to  allow  tubes  to  enter.  The 
lower  casting  carries  a  screw  thread  in  which  works  a  large 
screw  rod  KL  supporting  a  cast  piston  P  inside  the  glass  cylin- 
der. This  piston  has  a  covering  of  linen  greased  with  tallow  : 
at  its  centre  is  a  small  packing-box  filled  with  oakum,  through 
which  moves  an  iron  rod//',  8  millimeters  in  diameter,  which 
screws  up  and  down  inside  the  large  rod  KL,  and  ends  outside 
with  the  knob/. 

The  small  bath  is  fixed  by  means  of  set  screws  to  a  cast  ver- 
tical support  NN'9  but  in  such  a  way  that  it  can  be  made  to 
move  along  the  slots  r  r', — which  is  convenient  for  adjusting 
the  tubes.  This  bath  is  otherwise  completely  filled  with 
thoroughly  dry  mercury. 

We  begin  by  determining  by  a  preliminary  experiment  the 
capacity  of  the  cylindrical  reservoir  AB  and  its  coefficient  of 
expansion.  We  determine  in  the  same  way  the  volume  of  the 
capillary  tube  from  C  to  E,  as  well  as  that  of  the  small  portion 
of  the  larger  tube  E a  down  to  a  very  fine  mark  scratched  upon 
this  tube  at  a.  We  then  dry  the  reservoir  completely  and  fill 
it  with  dry  air  :  for  this  the  drawn-out  end  of  the  tube  is  con- 
nected with  the  drying  apparatus,  Fig.  4,  page  75,  and  the  whole 
length  of  the  reservoir  and  tube  are  warmed  with  hot  coals. 
A  vacuum  is  produced  a  great  many  times  and  each  time  the 
air  is  allowed  to  enter  again.  The  hot  coals  are  then  removed, 
there  being  free  communication  with  the  atmospheric  air. 
When  the  reservoir  has  cooled,  it  is  placed  in  very  cold  water 
or  even  in  some  ice  ;  finally,  after  some  time,  the  tip  of  the 
tube  is  closed  by  means  of  the  blowpipe. 

The  cast  upright  NN'  carries  a  cast  bracket-arm  FF ' F" 

90 


EXPANSION    OF    GASES 

fastened  with  screw  bolts  in  the  slots  cut  in  the  upright  NN'; 
it  can  thus  be  adjusted  at  various  heights.  To  this  bracket- 
arm  is  fastened  permanently  the  copper  cover  GG  of  a  vessel 
of  the  same  metal  GHH'G.  The  cover  is  provided  with  two 
tubulures  /,  /' :  in  one  the  reservoir  of  air  AB  is  fixed  by  means 
of  a  cork  ;  in  the  other  is  placed  a  mercury  weight-thermometer 
A'B',  of  exactly  the  same  shape  and  dimensions  as  the  air 
reservoir.  The  two  tubes  rest  upon  a  small  cross  piece  A  A 
fastened  to  the  rod  JJ'. 

The  tube  EF  is  introduced  into  the  tubulure  I7 and,  in  order 
to  fasten  it  hermetically,  is  wrapped  with  a  strip  of  linen 
greased  with  tallow,  which  is  then  forced  by  means  of  the  screw 
cap  E  into  the  annular  space  formed  in  the  tubulure.  We  thus 
obtain  an  air-tight  connection  which  will  resist  very  great  pres- 
sure. The  point  of  the  tube  UF  is  then  broken  off  by  means 
of  an  iron  rod  introduced  through  the  second  tubulure  T',  and 
in  this  second  tubulure  is  fastened,  in  exactly  the  same  way,  a 
piece  of  barometer  tubing  00',  perfectly  cylindrical  through- 
out its  length  and  of  exactly  the  same  diameter  as  the  end 
tubing  EF  possesses  below  where  it  is  drawn  out.  Besides  it 
was  shown  by  direct  experiment  that  there  was  no  difference 
between  the  capillary  depressions  in  the  two  tubes. 

To  conduct  the  experiment,  the  two  reservoirs  AB,  A  B'  are 
surrounded  with  melting  ice  which  is  put  in  a  small  bag  and 
hung  from  the  copper  cover  GG' .  By  turning  the  rod  KL  the 
piston  is  forced  up  until  the  mercury  comes  to  rest  at  a  in  the 
tube  EF;  the  fine  adjustment  is  made  with  the  aid  of  the  thin 
rod  f.  A  determination  of  the  difference  of  level  is  then  made 
with  the  cathetometer,  and  at  the  same  time  the  barometric 
pressure  is  recorded. 

The  ice  and  the  bag  which  contains  it  are  then  removed,  the 
vessel  GHH'G'  is  fastened  by  means  of  screws  to  its  cover  GG', 
and  the  water  which  it  contains  is  then  raised  to  boiling.  By 
pushing  up  the  piston  the  mercury  is  maintained  at  the  level  a 
in  the  tube  EF.  When  it  is  certain  that  the  air  has  come  to 
the  temperature  of  the  vapor,  the  mercury  level  is  adjusted 
exactly  at  a  by  means  of  the  rods  KL  andjf ',  and  the  difference 
of  level  of  the  two  columns  of  mercury  is  read  with  the  cathe- 
tometer, as  well  as  the  height  of  the  barometer. 

91 


MEMOIRS     ON 

I  made  some  experiments  at  first,  taking,  as  Rudberg  did, 
the  point  a  upon  the  capillary  stem  ;  but  I  found  that  it  was 
very  difficult  by  this  method  to  get  accurate  results.  Thus, 
although  in  one  experiment  the  tube  was  of  more  than  1  mm. 
diameter,  the  movement  of  the  mercury  in  the  tube  was  very 
irregular,  by  reason  of  the  variation  in  the  capillary  action. 
Sometimes  the  column  in  00  would  rise  more  than  1  mm., 
without  the  mercury  at  a  being  displaced  to  a  visible  extent  ; 
in  the  same  way,  on  lowering  the  piston,  the  column  had  often 
fallen  several  millimeters  in  the  tube  00',  while  the  meniscus 
at  a  had  only  become  flattened  ;  this  sluggishness  was  not 
entirely  overcome  by  even  quite  sharp  taps  given  the  appara- 
tus. 

It  became  necessary  to  take  the  point  a  upon  the  larger  tubing 
EF.  As  this  tubing  was  of  exactly  the  same  diameter  as  the 
barometer  tubing  there  was  no  correction  to  introduce  for  cap- 
illarity; but  it  was  necessary  to  take  account  of  the  small  vol- 
ume of  air  which  was  not  heated. 

Let  P  be  the  weight  of  mercury  at  0°  filling  the  reservoir  AB 
up  to  C  when  it  is  at  0°; 

p  the  weight  of  mercury  which  flows  out  at  the  temperature 
of  water  boiling  under  the  pressure  H',  or  at  the  tempera- 
ture T1-, 

p'  the  weight  of  mercury  which  fills  the  capillary  tube  CDE 
and  the  part  Ea  of  the  larger  tubing  EF; 

H  the  barometric  pressure  at  the  time  when  the  reading  is 
made,  the  reservoirs  being  kept  at  0°  by  melting  ice; 

h  the  difference  of  level  of  the  two  columns  of  mercury; 

t  the  temperature  of  the  surrounding  air. 
In  the  same  way  let  us  represent  by 

H'  the  barometric  pressure  when  the  reservoirs  are  heated  by 
boiling  water; 

T'  the  corresponding  temperature  of  the  vapor; 

h'  the  difference  of  level  of  the  two  columns; 

t'  the  temperature  of  the  air. 

Evidently  we  shall  have  the  equation 


hence 

92 


EXPANSION    OF    GASES 

aT==  d  +  J 

~ 


for,  by  reason  of  the  small  value  of  £    we   can   always   assume 

that  t  =  t. 

I  shall  again  here  distinguish  as  many  series  of  experiments 
as  special  pieces  of  apparatus. 

I.  An  experiment  made  to  determine  the  volume  of  the  air 
reservoir  and  its  coefficient  of  expansion,  gave 

P=  1975.862  gr., 
p  =      29.852, 
Hi  =    745.51  mm., 
Ti  =      99.46°, 
whence  100  6  =        0.002555. 

By  measurement,  there  was  found  for  the  weight  of  mercury 
filling  the  capillary  tube  and  the  small  piece  of  larger  tubing 
as  far  as  the  mark, 

P  =  9.740  gr., 

whence  P   —  0.00493. 

P 

The  tube  being  heated  by  the  vapor  of  boiling  water,  two 
readings  made  with  a  half-hour  interval  gave 
H'  ...........  751.01  751.01 

/*'  ...........  296.70  296.70 

t'  ...........       8.6°  8.8° 

T  ...........     99.66°  99.66° 

whence  H'+h'=      1047.71  1047.71 

The  reservoir  being  in  melting  ice,  we  have 

H  ...........  .749.98  749.88  749.78 

h  ............  20.53  20.59  20.63 

t  ............     8.5°  8.5°  8.5° 

H+h  .........  770.51  770.47  770.41 

We  shall  take  as  an  average 

H+h  =  770.47. 

Comparing  this  mean  with  the  two  determinations  at  the 
boiling  point  of  water,  we  have  [the  ratios] 

1.36688,  1.36688. 

A  second  series  of  experiments  made  with  this  apparatus 
gave: 

The  tubes  being  in  melting  ice, 

93 


ME  MO  IB  8    OK 


H 746.16 

h 24.53 

t 8.3° 

H+  h' 770.69 


746.26 
24.41 

8.3° 
770.67 


746.39 
24.21 

8.3° 
770.60 


746.61 
24.11 

8.3° 
770.72 


746.66 

24.09 

8.3° 

770.75 


Mean  of  H  +  h  =  770.69. 

Iu  boiling  water  we  have: 

741.01 
305.62 
9.00° 
99.29° 
1046.63 


741.14 

743.20 

743.26 

305.36 

303.72 

303.64 

9.00° 

9.00° 

9.00° 

99.29° 

99.37° 

99.37° 

1046.50 

1046.92 

1046.90 

H' 740.79 

h' 305.58 

*' 9.00° 

T 99.28° 

H'  +  hf 1146.37 

On  comparing  each  of  the  values  of  H'  +  li  with  the  mean 
770.69  of  the  determinations  in  melting  ice,  we  have  [the 
ratios]: 

1.36612 

1.36643 

1.36626 

1.36651 

1.36649 


Mean  = 


=  1. 


II.     With  a  second  apparatus  made  with  a  reservoir  cut  from 
the  same  piece  of  tubing  as  the  former,  we  have 


assuming 


P=  1817.50  gr.; 

100  (J=  0.002555, 

p*  =  8.50  gr., 

P' 

"F  = 


0.00468. 


In  melting  ice  we  have: 


H. 


t 

H  +  h.... 


752.60 

752.60 

752.65 

752.57 

752.40 

752.25 

19.58 

19.58 

19.76 

19.66 

19.74 

20.24 

11.0° 

11.0° 

11.0° 

ll.t)° 

11.0° 

11.0° 

772.18 

772.18 

772.41 

772.23 

772.14 

772.49 

Mean  of  H  +  h  =  772.29. 


In  boiling  water  we  have: 


H' 

h' 

If 


751.15 

299.16 

13.7° 

1050.31 

99.67° 


751.13 
299.66 

1050.79 


751.13 
299.66 

1050.79 


751.08 
299.76 

1050.84 


751.05 
299.86 

1050.91 


EXPANSION    OF    GASES 

The  five   values   of   H'  4-  h',  compared  with   the   mean   of 
H+h,  give  [the  ratios]  : 

1.36672 
1.36714 
1.36714 
1.36730 
1.36747 

Mean  =      6'8f77     =  1.36715. 
5 

Thus  the  three  series  of  experiments  made  by  this  method 
gave  the  following  mean  values: 

1.36688 
1.36636 
1.36715 


A 

General  mean  =      *'  „      -  =  1.36679. 
o 

This  average  differs  little  from  that  found  in  the  two  former 
series. 

I  do  not  think  this  method  leads  to  the  same  accuracy  as  the 
others  which  I  have  used.  The  tubes  in  which  the  columns  of 
mercury  are  measured,  are  not  of  large  enough  diameter  to 
make  the  capillary  effect  negligible;  the  capillary  depression 
amounts  in  these  tubes  to  about  1  mm.  This  capillary  depres- 
sion, theoretically,  does  not  enter  into  the  calculation  of  the 
constant,  and,  if  it  remains  always  the  same,  it  exerts  no  influ- 
ence. Yet  it  is  easy  to  show  that  this  effect  must  vary  between 
rather  wide  limits,  by  measuring  from  time  to  time  the  heights 
of  the  tops  of  the  menisci  ;  we  may  thus  realize  that  these 
sometimes  vary  in  the  same  experiment  from  a  certain  amount 
to  double  that  amount.  As  a  matter  of  fact,  here  is  a  series  of 
measurements  of  the  corresponding  heights  of  the  two  menisci: 

Tube  EF  Tube  00' 

1.08  mm.  1.14  mm. 

0.72  1.64 

1.00  1.64 

1.10  1.32 

1.38  1.36 

0.96  1.20 

0.80  1.18 

It  is  not  possible  that  such  marked  variations  in  the  heights 
of  the  menisci  do  not  involve  very  considerable  changes  in  the 
capillary  depressions. 

95 


MEMOIRS    ON 


Rudberg  with  his  apparatus  has  found  lower  figures  than 
mine.  It  is  difficult  with  any  certainty  to  determine  the  causes 
of  these  differences.  I  have  already  stated  above  that  I  had 
never  obtained  good  results  when  I  fixed  the  mark  «  on  the 
capillary  part  ED  of  the  tube;  but  I  believe  that  still  another 
reason  could  be  given  which  has  led  Rudberg  to  results  that 
are  too  low.  This  physicist  has  always  in  his  calculations  neg- 
lected the  little  volume  of  air,  not  heated,  which  is  contained 
in  the  portion  Ba  of  his  capillary  tube.  This  volume  is  very 
small,  nevertheless  it  is  hardly  probable  that  it  can  be  entirely 
neglected.  Unfortunately,  Rudberg  has  not  given  in  his  mem- 
oir the  dimensions  of  the  different  parts  of  his  apparatus; 
hence  it  is  impossible  to  calculate  now  the  correction  this  fact 
would  involve  in  his  results. 

FOURTH  SERIES  OF  EXPERIMENTS. 
This  series   of   experiments   was  made   with   an   apparatus 


EXPANSION    OF    GASES 

which  served  the  same  end  as  that  of  the  preceding  series, 
without  possessing  the  same  disadvantages.  It  consists  of  a 
large  bulb  A  (Figs.  13  and  14)  of  800  to  1000  cubic  centimet- 
ers' capacity,  to  which  is  sealed  a  capillary  tube  about  20  centi 
meters  in  length.  This  bulb  serves  as  the  air-reservoir  and 
must  be  brought  successively  to  0°  and  to  100°;  it  is  put  in 
communication  with  a  syphon  tube  full  of  mercury,  which 
serves  to  measure  the  tension  of  the  air. 

A  tube  JI  of  16  to  17  mm.  internal  diameter,  perfectly  cyl- 
indrical, is  fastened  by  means  of  gum- mastic  in  an  iron  cast- 
ing IH provided  with  a  tap  K.  This  carries  a  side  tubulure  H 
in  which  is  cemented  a  second  tube  HGFE  of  the  same  diame- 
ter as  the  first  throughout  the  length  FG.  This  tube  ends  at 
the  top  in  a  bent  capillary  tube  FED,  cut  from  the  same  capil- 
lary tubing  as  the  tube  BC  sealed  to  the  bulb.  The  tube  BC 
fits  close  in  a  small  copper  three-way  tube  mno  in  which  it  is 
firmly  fastened  with  mastic.  In  the  second  arm  o  is  cemented 
a  short  piece  of  capillary  tubing  op  which  has  been  drawn  out 
at  its  end  p. 

The  system  of  the  two  tubes  IJ  and  EH  is  fastened  to  a 
plank  which  is  itself  firmly  secured,  and  in  a  perfectly  vertical 
position,  to  a  cast-iron  upright  LL'. 

The  bulb  A  is  fastened  once  for  all  in  a  vessel  of  tin  plate 
MN,  in  which  water  can  be  boiled,  or  the  bulb  surrounded 
with  ice.  This  vessel  rests  upon  an  iron,  tripod  PQQ'P'.  A 
furnace  0  upon  a  support  S  can  be  put  below  the  vessel  MN 
and  withdrawn  at  will. 

This  is  now  the  way  an  experiment  is  made.  The  open  end 
of  the  tube  op  is  connected  with  the  drying  apparatus  (Fig.  4) 
[page  75];  and  in  order  to  close  the  arm  n  of  the  copper 
tube,  a  bit  of  tubing  completely  closed  is  attached  to  it  with  a 
piece  of  rubber  tubing.  The  water  in  the  vessel  MN  is 
brought  to  boiling,  and  a  vacuum  is  produced  a  great  many 
times  within  the  bulb,  each  time  allowing  the  air  to  enter  again 
very  slowly. 

The  tube  HGFED  had  been  dried  at  a  high  temperature  in 
the  same  way  before  being  cemented  in  the  tubulure  H,  and 
very  dry  mercury  is  immediately  poured  into  the  tube  JI,  so 
as  to  fill  completely  the  tube  ffGFup  to  the  open  end  D.  In 

97 


MEMOIRS     ON 

this  way  moisture  is  kept  out  of  this  tube.  With  the  same  idea 
care  is  taken  to  keep  the  end  of  the  tube  D  covered  with  a  cap 
of  rubber. 

The  bulb  A  being  filled  with  very  dry  air,  the  bit  of  stopped- 
up  tubing,  which  during  the  drying  was  over  the  tubulure  nt  is 
removed,  and  the  capillary  tube  DE  is  connected  with  this  tu- 
bulure by  means  of  rubber;  this  tube  fits  closely  in  the  copper 
tubulure  and  comes  butt-to-butt  against  the  tube  BC,  so  that 
within,  the  little  copper  three-way  tube  mno  the  only  space 
there  is  is  the  bore  of  the  capillary  tubes  which  meet  there.  At 
other  times  the  tube  DE  is  fastened  in  the  tubulure  by  means 
of  mastic. 

The  tap  K  is  opened;  the  mercury  which  flows  out  is  re- 
placed in  the  tube  EFG  by  air  which  has  passed  through  the 
drying  apparatus.  The  mercury  is  run  out  until  the  level 
stands  in  the  tube  FG  at  a  mark  a  scratched  on  the  glass.  The 
mercury  stands  at  the  same  level  in  the  two  tubes,  since  on 
both  sides  it  is  freely  open  to  the  air. 

The  drying  apparatus  is  now  disconnected  and  the  tip  p  of 
the  tube  op  is  closed  by  means  of  a  lamp.  At  the  same  time 
the  height  H  oi  the  barometer  is  recorded. 

The  furnace  which  keeps  the  water  boiling  in  the  sheet-iron 
vessel  is  removed.  In  order  that  the  bulb  A  may  become  cool 
more  rapidly,  the  hot  water  is  drawn  off  by  opening  the  tap  R; 
the  cover  abcdefgh  is  taken  off  and  cold  water  is  poured  several 
times  into  the  vessel  to  cool  the  walls.  Finally  the  bulb  A  is 
completely  covered  with  crushed  ice,  which  is  kept  in  place  by 
a  cloth  fastened  to  the  edge  cd  of  the  vessel. 

The  air  contracts  on  cooling,  the  mercury  rises  in  the  tube 
GF;  but  it  is  maintained  at  the  same  level  a  by  running  out 
some  of  the  mercury  through  the  tap  K. 

When  it  is  certain  that  the  air  in  the  bulb  A  has  come  to 
the  temperature  of  melting  ice,  the  barometric  height  H'  is  re- 
corded, and  the  difference  of  level  aP  =  h'  is  measured  by 
means  of  the  cathetometer.  We  thus  have  already  all  the 
data  necessary  for  determining  the  rate  of  expansion  of 
air;  but  we  can  get  a  second  determination  in  the  following 
way: 

The  closed  tip  p  is  again  connected  with  the  drying  appara- 

98 


EXPANSION    OF    OASES 

tus;  "this  apparatus  is  exhausted  several  times  in  succession,  to 
make  sure  that  it  is  full  of  dry  air;  then  the  tip  p  is  broken  off. 
The  mercury  now  falls  in  the  tube  FG,  but  it  is  brought  back 
to  a  by  pouring  mercury  into  the  tube  JI. 

After  some  time  the  tip^?  is  again  closed  by  means  of  a  lamp 
and  the  height  H"  of  the  barometer  is  recorded.  The  ice  is 
then  removed;  the  cover  abed  of  the  tin  vessel  is  put  back,  and 
the  water  poured  into  the  vessel  is  brought  to  boiling  once 
more.  By  pouring  mercury  into  the  tube  IJtlcie  level  is  main- 
tained at  a  in  the  tube  FG.  After  the  bulb  has  remained  about 
an  hour  in  [the  vapor  of]  the  boiling  water,  [the  height  of]  the 
barometer  H'"  is  noted,  and  the  difference  of  level  ay  =  h'"  of 
the  mercury  in  the  two  columns  is  measured. 

In  the  calculation  of  the  experiment  it  is  necessary  to  take 
account  of  the  small  volume  of  air  that  remains  constantly  at 
the  temperature  of  the  surrounding  air.  For  this  we  must 
know  the  ratio  of  this  volume  to  that  of  the  bulb  A.  The 
latter  volume  V  had  been  determined  by  measurement  with 
distilled  water,  and  the  volume  v  of  the  air  contained  in  the 
capillary  tubes  BC,  DEF,  op,  as  well  as  in  the  part  Fa  of  the 
larger  tube,  had  been  found  by  measurement  with  mercury. 
We  thus  had: 

Weight  of  mercury  filling  F=  9889.9  gr., 
ditto ditto v=     26.85; 

hence  £.  =  0.002715. 

I  was  not  able  directly  to  determine  the  coefficient  of  expan- 
sion of  the  bulb  A;  it  would  have  been  necessary,  for  this,  to 
have  boiled  a  mass  of  9  to  10  kilograms  of  mercury  in  a  bulb 
of  glass  ending  in  a  capillary  tube,  which  seemed  to  me  a  prac- 
tically impossible  operation.  I  have  assumed  the  figure  0.00233 
for  this  coefficient,  which  is  the  mean  of  those  found  for  the 
two  bulbs  used  in  my  Second  Series  of  determinations.  These 
bulbs  were  the  product  of  the  same  factory  and  were  of  the 
same  kind  of  glass. 

The  temperatures  t,  t',  t",  t"' ',  of  the  small  volume  of  air  v 
were  indicated  by  the  small  thermometer  T' ;  that  of  the  col- 
umns of  mercury  by  the  thermometer  T  whose  cylindrical 
reservoir  had  the  same  diameter  as  the  tubes  IJ  and  FG. 

99 


MEMOIKS    OK 


The  equation  which  serves  for  the  first  half  of  the  experi- 
ment is  the  following: 

(1  +  6  T)  H 


H'-h'-  £ 


+  at 


[H  —  II'  +  /*'] 


that  which  applies  to  the  second  half  is 

(l  +  ST")  H'"  +h' 


1+  a  T"  =- 


TJ,, 

-a     —  TT- 


+  h'"  —  H"] 


We  have  assumed  in  these  equations 

t  =  t'  and  t" =1"'. 

We  now  have  the  figures  obtained  by  this  method: 

First  Half. 


H 

T 

t 

H' 

V 

f 

14  lOOa 

I 

747.83 

99.55° 

14.0° 

747.43 

197.49 

14.0° 

1.36592 

2 

742.27 

99.34° 

13.9 

744.25 

198.56 

13.5° 

1.36710 

3 

747.97 

99.55° 

13.0 

748.52 

198.76 

12.5° 

1.36662 

:  —  ^  ^  — 

Mean l.J 


Second  Half. 

H" 

t" 

H'" 

T'" 

h'» 

t'" 

1  +  100  a 

1 

747.30 

14.2° 

746.45 

99.50° 

270.28 

15.1° 

1.36682 

2 

744.59 

13.1° 

745.27 

99.45° 

267.59 

15.6° 

1.36674 

3 

748.72 

12.9° 

749.19 

99.59° 

269.59 

13.9° 

1.36580 

Mean..                  ..1.36645 

Thus  the  mean  of  the  six  determinations  is  1.3665. 

In  the  Fourth  Method  the  expansion  of  the  air  is  measured 
under  very  different  pressures  :  in  fact,  in  the  first  half  of  each 
experiment  the  air  was  under  a  pressure  of  only  about  0.550  m. 
when  at  0°,  and  under  the  atmospheric  pressure  0.760  m.,  when 
heated  to  100°.  In  the  second  half,  the  air  at  0°  is  under  the 
atmospheric  pressure  0.760  m.,  and  the  air  heated  to  100°  is 
under  a  pressure  of  about  1.040  m.  As  the  experiments  show  no 
difference  in  the  numbers  obtained  in  the  two  halves,  it  must 
be  concluded  that,  within  these  pressure  limits,  dry  air  shows 
a  practically  constant  coefficient  of  expansion. 

It  is  very  easy  to  arrange  the  apparatus  so  that  it  will  serve 
for  the  study  of  the  expansion  of  air  under  greater  pressures  ; 
in  fact,  it  will  suffice  for  this  to  give  the  tube  EFGH  &  con- 
siderable capacity  from  a  certain  point  6  to  H,  Fig.  15,  sealing 
the  tip  p  at  the  time  when  the  bulb  as  well  as  the  tube  EH  as 
far  as  H  are  full  of  dry  air,  then  pouring  mercury  into  the  tube 

100 


EXPANSI'O'N'  OF  GASES 


//until  the  mercury-level  coincides  with  a  in  the  tube  FaG,  the 
bulb  being  surrounded  with  melting  ice  ;  the  mercury  then 
rises  in  the  tube  1J  a  certain  distance  h,  so  that  the 
volume  of  gas  is  then  at  0°  under  a  pressure  H-\-h. 
The  bulb  being  raised  to  100°,  in  order  to  keep  the 
level  of  the  mercury  at  a  in  the  tube  FG,  it  is  neces- 
sary to  pour  a  new  lot  of  mercury  into  the  tube  //, 
which  gives  a  difference  of  level  h'  and,  consequently,  E 
for  the  pressure  upon  the  gas  at  100°,  H-^li'.  The  F 
heights  li  and  h1  will  be  more  considerable  as  the  a 
volume  of  the  tube  6H  is  greater  in  proportion  to 
the  volume  of  the  bulb.  Some  experiments  made  by 
the  method  thus  modified  will  be  discussed  later.1 

1  1  have  also  made  some  experiments  to  determine  the 
coefficient  of  expansion  of  air  by  the  method  of  M.  Gay- 
Lussac.  This  method  consists,  as  is  well  known,  in  observ- 
ing the  expansion  suffered  by  dry  air  enclosed  in  an  actual 
thermometer,  this  air  being  separated  from  the  outside  air 
by  a  tiny  index  of  mercury. 

The  capillary  tube  was  measured,  then  graduated  with 
the  greatest  care  ;  it  was  of  2.7  mm.  bore  and  was  marked 
with  600  divisions  in  a  length  of  558  mm.  The  experiment 
was  begun  by  filling  this  thermometer  with  mercury  which 
was  again  and  again  brought  to  boiling  in  the  bulb  and  in  FIG.  15 
the  tube,  then  was  entirely  surrounded  with  ice;  the  point  where  the 
mercury  came  to  rest  on  the  scale  was  noted.  A  portion  of  the  mercury 
in  the  stem  was  made  to  flow  out  and  was  weighed,'  then  the  ther- 
mometer was  once  more  put  in  the  ice  and  the  point  noted  where  the 
column  came  to  rest.  This  operation  repeated  three  times  in  different 
parts  of  the  scale,  gave  the  following  results  : 

Mercury  at  0°  between  375.8  and   602.0  =  226.2  div.;  6.629  gr. 
103.0  375.8  =  272.8  7.9945 

50.9  499.0  --=448.1  13.128 

From  this  we  deduce  for  the  weight  of  mercury  at  0°    occupying  owe 
division  : 

in  the  first  interval  ........  ............  0.029306  gr. 

in  the  second  .........................  0.029305 

in  the  third  ...............    ...........  0.029297 


Mean     =     o_jL8_72JLS.  =  0.029303. 

The  close  agreement  to  be  noticed  in  these  figures  proves  satisfactorily 
the  accuracy  of  the  graduation. 

The  mercury  which  at  0°  filled  the  bulb  and  the  stem  as  far  as  divi- 
sion 50.9,  weighed  27.916  gr. 

101 


l£$    ON 

The  four  series  of  experiments  which  I  have  described  in 
detail  have  therefore  given  the  following  averages  : 

After  the  mercury  has  been  completely  removed  from  the  apparatus, 
it  is  connected  by  means  of  rubber  tubing  with  a  U-shaped  tube  con- 
taining pumice  stone  moistened  with  sulphuric  acid  and  is  exhausted  a 
great  many  times  while  being  warmed  by  means  of  hot  coals.  This 
thermometer  tube  was  fitted  at  the  end  with  a  bit  of  larger  tubing  in 
which  had  been  left  a  tiny  drop  of  mercury  to  form  the  index.  The 
apparatus  being  filled  with  dry  air,  the  bulb  is  raised  to  such  a  tempera- 
ture that  the  globule  of  mercury,  when  drawn  into  the  capillary  tube, 
comes  to  rest  at  a  convenient  point  when  the  thermometer  is  placed  in 
melting  ice. 

The  greatest  pains  were  taken  to  place  the  stem  of  the  thermometer 
in  a  perfectly  horizontal  position  where  the  instrument  was  in  ice  or  in 
[the  vapor  of]  boiling  water,  and  it  was  given  light  taps  to  assist  the 
movement  of  the  index. 

I  shall  not  describe  in  detail  the  numerous  experiments  made  by  this 
method  ;  suffice  it  to  say  I  was  unable  to  get  constant  figures.  The  way 
in  which  the  thermometer  tube  was  tapped,  the  points  on  the  tube 
where  it  was  struck,  produce  a  very  marked  effect  upon  the  position  of 
the  index.  The  movement  of  the  index  even  seemed  to  depend  upon 
the  more  or  less  rapid  changes  of  the  temperature,  which  seems  to  show 
that  the  mercury  index  does  not  close  the  tube  perfectly,  and  that 
would  not  be  surprising  after  what  we  have  seen  above  [page  80]. 
What  confirms  me  in  this  opinion  is  that,  in  many  experiments,  the 
index  did  not  return  to  the  same  point,  the  thermometer  being  sur- 
rounded with  ice,  when,  in  the  interval,  the  apparatus  had  been  heated 
to  the  boiling  point  of  water. 

Thus,  in  one  experiment,  the  index  came  to  rest  when  the 
thermometer  was  in  ice,  at 152.7  div. 

In   [the  vapor  of]   boiling  water  at  534.5  div. ;  the  appara- 
tus being  again  surrounded  with  ice,  the  index  came  to  rest  at.  .154.5  div. 
and  meantime  the  barometer  had  not  changed  to  any  noticeable  extent. 

In  another  experiment  the  index  came  to  rest  in  melting  ice  at  66.5 
div.  before  the  instrument  had  been  put  in  [the  vapor  of]  boiling  water, 
and  at  66.0  div.  after  it  had  been  heated.  The  barometer  had  changed 
in  a  very  marked  way  during  the  interval,  but  this  change  should  have 
produced  a  movement  in  the  opposite  direction. 

However  that  may  be,  here  are  some  of  the  figures  I  obtained  by  this 
method :  1.3641 

1.3626 
1.3635 
1.3647 
1.3552 

It  is  remarkable  that  all  these  figures  are  smaller  than  those  yielded 
by  the  other  methods.  This  circumstance  is  probably  the  result  of  mere 
chance. 

102 


EXPANSION    OF    GASES 

First  series  ................................  1.36623  ; 

Second  series  ..............................  1.36633  ; 

Third  series  ...............................  1.36679  ; 

Fourth  series  ..............................  1.36650  ; 

That  is  to  say,  about  .....................  1.3665. 

I  therefore  propose  to  adopt  for  the  coefficient  of  expansion 
of  dry  air  for  each  degree  centigrade  between  the  two  fixed 
points  of  the  thermometer,  0.  003665.  1 

We  shall  now  proceed  to  take  up  in  succession  all  the  quan- 
tities which  enter  into  the  calculation  of  the  experiments,  in 
order  to  obtain  an  approximate  value,  at  least,  for  the  error 
each  of  them  may  introduce. 

The  equation 

•  P'(l+*T)H 

~(P'  —  P)  (H'—h)\ 

which  applies  to  the  first  two  series,  comprises  the  weights  P 
and  P'  of  mercury  which  can  be  determined  with  what  may  be 
called  absolute  precision.  Thus  the  factor  pf_p  cannot  intro- 
duce any  noticeable  error  arising  from  its  experimental  deter- 
mination. 

The  factor  1  -\-6T  depends  upon  the  expansion  of  the  glass. 
We  have  seen  that  this  expansion  was  determined  for  each  ap- 
paratus by  direct  experiment  and  it  must  be  admitted  to  be 
rigorously  exact;  besides,  since  it  is  very  small,  a  noteworthy 
error  in  this  coefficient  would  exert  no  appreciable  effect  upon 
the  value  of  the  coefficient  of  expansion  of  air. 

The  coefficient  of  expansion  of  glass  was  determined  as  being 
a  function  of  the  coefficient  of  expansion  of  mercury;  I  have 
assumed  for  the  latter  coefficient  the  value  ^.5  =  0.01802, 
found  by  Dulong  and  Petit.  Unfortunately,  some  uncertainty 
exists  regarding  the  numerical  value  of  this  coefficient;  in  fact, 
Dulong  and  Petit  gave  in  their  memoir  only  the  following 
values: 

Expansion  of  mercury  for  each  degree  centigrade  between 

0°  and  100°, 
ditto  ................  ditto  ......  0°  and  200°, 

ditto  ................  ditto  .......  0°  and  300°, 


1  M.  Babinet  has  called  my  attention  to  the  fact  that,  adopting  for  the 
coefficient  of  expansion  of  air  the  figure  0.366666.  .  .  ,  this  coefficient 
may  be  represented  by  the  very  simple  fraction  fo,  which  is  very  easy  to 
use  in  calculations. 

103 


MEMOIRS    ON 

The  temperatures  are  given  here,  as  these  distinguished  phys- 
icists explicitly  state,  with  reference  to  the  air  thermometer, 
assuming  for  the  coefficient  of  expansion  0.375;  but  if  this  co- 
efficient is  inaccurate  and  if  the  figure  0.3665  must  be  used, 
then  the  intervals  of  temperature  change  appreciably  and  the 
temperature  100°  of  Dulong  becomes  102.7° ,  so  that  the  coeffi- 
cient 5^  should  be  about  -fa  greater.1 

It  is  possible,  however,  that  the  coefficient  of  absolute  expan- 
sion of  mercury  between  0°  and  100°  given  by  Dulong  and 
Petit  may  be  that  which  they  found  directly  in  their  experi- 
ments from  [the  temperature  of]  melting  ice  up  to  [that  of] 
boiling  water,  without  deducing  it  from  their  interpolation-for- 
mula. In  this  event  it  would  not  be  affected  by  the  same 
source  of  error  as  the  values  between  0°  and  200°  and  between 
0°  and  300°.  However  that  may  be,  new  experiments  alone 
can  decide  the  point. 

What  interests  us  at  this  moment  is  to  see  what  difference 
this  could  bring  about  in  our  coefficient  of  expansion  of  air. 
Assuming  the  coefficient  of  absolute  expansion  of  mercury  be- 
tween 0°  and  100°  too  great  by  -fa,  the  coefficient  of  expansion 
of  glass  would  be  too  great  by  about  -j^.  Thus,  instead  of  the 
figure  1.0026,  we  should  have  in  the  numerator  the  figure 
1.0024,  smaller  than  the  former  by  To,^o,  which  would  reduce 
the  figure  1.3665  by  y^oo*  that  is  to  say,  would  give  1.3662; 
consequently  this  change  would  affect  only  the  fourth  decimal: 
after  all,  it  is  a  correction  easily  made  in  all  my  figures. 

TT 

The  factor  H,_h  which  depends  upon  the  barometric  mea- 
surements, is  the  one  which  is  liable  to  the  largest  errors  of  ob- 
servation. Physicists  who  have  had  occasion  to  make  a  large 
number  of  barometric  observations,  know  how  difficult  these 
observations  are  when  the  attempt  is  made  to  reach  the  high- 
est limit  of  accuracy.  I  do  not  believe  I  exaggerate  when  I 
take  it  for  granted  that  a  barometric  reading  cannot  be  made 
closer  than  ^  of  a  millimeter,  however  improved  the  measur- 
ing apparatus  may  otherwise  be.  The  difficulty  lies  in  the  fact 
that  the  atmospheric  pressure  is  constantly  changing,  bat  this 

i  This  point  has  already  been  made  by  M.  Poggendorif,  Poggendorff's 
Annalen,  Yol.  XLI,  page  467. 

104 


EXPANSION     OF     GASES 

variation  is  at  once  shown  by  the  barometer,  yet  as  a  rule, 
only  the  changes  in  the  form  of  the  meniscus,  and  the  varia- 
tions in  height  do  not  take  place  in  any  regular  way,  but 
rather  by  jerks.  It  is  well,  in  order  to  avoid  this  trou- 
ble, to  tap  the  barometer  to  make  the  mercury  column 
move  back  and  forth,  before  making  a  reading,  yet  it  is 
clear  that  the  source  of  error  is  not  completely  done  away  with 
by  this  means. 

Each  of  the  measurements  H,  H',  h,  is  liable  to  the  same  er- 
ror e.  In  order  to  determine  the  maximum  deviation  of  indi- 
vidual experiments,  we  shall  suppose  the  errors  made  in  H,  H',  h, 
to  have  such  signs  as  will  produce  the  greatest  difference  in 
the  final  result.  Thus,  we  will  assume  that  instead  of  the 

rr 

accurate  factor  H,_fl ,  observation  has    given   us  the  factor 

H+e 


(H'-e)  - 

The  error  is  then  represented  by 


or 

e  (2  ff4  H'  —  h) 


(H'—h)  (H'  —  h-2e) 
or  simply 

2H+H'  —  h 
(H'  —  h)*    ' 

by  neglecting  2e  in  the  denominator  in  comparison  with  H' — h. 
As  a  result,  the  value  of  1  +  aT  becomes 


,  a 


_ 
(P'  —  P)     JET  —  h  I-  H'  —  h 

Assuming  H  =  H'  =  760  mm.,  h  =  190  mm.;  we  shall  have 
for  the  last  factor 

760.00  mm.  +  e.    209°  , 
or  570  ' 

760.00  mm.  +  e  x  3.67. 

If  e  =  0.1  mm.,  then  the  total  error  resulting  for  760.00  mm. 
will  be  0.367  mm.,  that  is  to  say  T<To*Wo- 

This  gives  for  the  total  possible  range  of  error  in  the  experi- 
ments, for  this  source  of  error  alone,  -njofinny- 

It  may  thus  be  seen  that  if  we  assume  it  impossible  to  attain 
H  105 


MEMOIRS    ON 

an  accuracy  greater  than  ^  of  a  millimeter  in  barometric  ob- 
servations, the  determinations  of  the  rate  of  expansion  of  air 
will  be  liable,  from  this  source  of  error  alone,  to  show  a  maxi- 
mum variation, of  about  T^oo»  Ik  will  be  noticed  that  this  is 
close  to  the  maximum  variation  to  be  observed  in  my  results. 

In  order  that  the  coefficient  of  expansion  of  air  may  be  exact 
up  to  the  third  decimal,  the  experiment  which  determines  it 
must  not  lead  to  an  error  of  more  than  T^oo-  The  direct  ex- 
periment does  not  tell  us,  as  a  matter  of  fact,  that  1000  parts 
of  air  expand  between  0°  and  100°  by  366  parts,  which  would 
be  an  accuracy  of  only  ^^;  but  rather  that  1000  parts  of  air 
become  1366  in  passing  from  0°  to  100°,  which  gives  an  accu- 
racy of  jsVe. 

The  formulas  which  apply  to  the  two  later  series  of  experi- 
ments are  evidently  open  to  the  same  sources  of  error.  The 
possible  error  in  the  measurement  of  the  heights  of  the  col- 
umns of  mercury  is  probably  even  greater  in  the  apparatus  of 
the  Third  Series,  since  the  tubes  are  narrower  and  on  this  ac- 
count show  a  greater  variability  in  the  capillary  depression. 

Yet  there  is  in  addition  another  source  of  uncertainty  in 
these  two  methods  which  did  not  enter  into  the  two  earlier 
ones:  it  lies  in  the  determination  of  the  temperature  of  the  vol- 
ume of  air  which  was  not  heated.  The  error  resulting  from 
this  might  be  quite  large  if  this  volume  formed  an  appreciable 
fraction  of  that  which  is  brought  to  the  fixed  points:  it  is  en- 
tirely negligible  in  my  experiments,  since  I  took  pains  to  carry 
them  out  so  that  the  volume  of  the  air  that  was  not  heated 
should  never  be  but  an  extremely  small  fraction  of  the  total 
volume. 

The  temperature  ^of  the  vapor  was  calculated  from  the  ob- 
served barometric  heights  at  the  time  of  the  boiling.  I  have 
assumed  in  this  calculation  that  a  variation  of  1°  in  the  boiling- 
point  of  the  water  corresponded  to  a  difference  of  pressure  of 
26.7  mm.  This  figure  is  that  given  in  the  tables  of  the  tensions 
of  water-vapor  recently  calculated  by  M.  Biot.  It  seemed  to 
me  better  to  adopt  this  figure,  than  to  take  the  numbers  found 
by  different  physicists  by  determining  with  some  one  ther- 
mometer the  boiling  point  of  water  under  various  barometric 
pressures.  These  experiments  could  not  result  in  great  accu- 

106 


EXPANSION    OF    GASES 

racy,  for  they  were  frequently  carried  out  on  days  quite  sepa- 
rated from  one  another,  and  because  the  instrument  had 
probably  already  suffered  some  appreciable  change  in  the  inter- 
val through  the  movement  of  the  fixed  points. 

In  order  that  these  experiments  should  yield  results  that 
could  not  be  questioned,  it  must  have  been  possible  to  take 
note  of  the  boiling  point  of  water  under  various  pressures,  at 
times  close  together,  for  example,  in  an  apparatus  where  the 
pressure  could  be  varied  at  will,  as  in  the  apparatus  of  M. 
Tabarie.  A  series  of  observations  might  even  be  made  during 
the  ascent  of  a  mountain  and  while  care  was  being  taken  to 
keep  the  thermometer  constantly  in  [the  vapor  of]  boiling 
water  during  the  ascent,  in  order  to  avoid  as  far  as  possible 
movement  of  the  fixed  points. 

However  that  may  be,  the  figure  I  have  assumed  must  be 
very  near  the  true  one,  and  the  error  which  could  be  produced 
by  it  in  the  coefficient  of  expansion  of  air  is  entirely  inappre- 
ciable. 

My  barometric  observations  were  made  with  a  barometer  with 
a  Fortin  cistern,  which  had  been  carefully  compared  in  a  series 
of  measurements,  with  that  of  .the  Paris  Observatory,  corrected 
for  capillary  depression,  and  all  my  observations  were  reduced 
by  calculation  to  [those  of]  the  Observatory  barometer. 

After  all,  a  small  constant  difference  in  the  absolute  values 
of  all  the  barometric  heights  would  have  had  no  appreciable 
effect  upon  the  coefficient  of  expansion  of  air,  since  it  would 
have  had  to  do  only  with  the  determination  of  the  temperature 
of  the  vapor,  and  its  influence  upon  the  other  would  be  quite 
inappreciable. 


PAET  II. 

Upon  the  Rate  of  Expansion  of  certain  other  Gases. 

The  old  coefficient  adopted  for  the  expansion  of  air  being  in- 
accurate to  the  extent  of  ^,  it  is  clear  that  it  cannot  be  con- 
sidered as  proved  that  all  gases  have  the  same  coefficient  of 

107 


MEMOIRS     ON 

expansion;  new  determinations  are  necessary  to  decide  whether 
this  law  is  strictly  true  or  is  only  approximate. 

I  have  made  experiments  upon  nitrogen,  hydrogen,  oxide  of 
carbon  [carbon  monoxide],  carbonic  acid,  sulphurous  acid, 
cyanogen,  protoxide  of  nitrogen  [nitrous  oxide],  hydrochloric 
acid  and  ammonia.  Most  of  these  determinations  were  made 
by  Method  II;  some  however  were  made  by  Method  IV. 

First,  I  shall  describe  in  a  few  words  how  the  experiment 
was  managed  when  Method  II  was  employed.  The  bulb  being 
suspended  in  the  steam  vessel  and  connected  with  the  drying- 
apparatus,  it  was  exhausted  many  times  and  the. air  allowed  to 
re-enter  slowly,  in  such  a  way  as  to  dry  the  bulb  thoroughly; 
then  to  the  second  tubulure  of  the  pump  was  attached  the 
apparatus  in  which  the  gas  was  produced.  The  bulb  being 
exhausted,  as  well  as  the  gas-generating  apparatus,  the  tap  is 
gradually  opened  so  as  to  allow  the  gas  to  enter  as  fast  as  it  is 
formed  :  the  progress  of  the  operation  is  indicated  by  a  safety 
tube  placed  somewhere  in  the  generating  apparatus.  When 
the  bulb  was  full  of  gas,  it  was  exhausted,  then  allowed  to  be- 
come full  of  gas  once  more,  and  so  four  or  five  times  in  succes- 
sion. In  other  respects  the  experiment  was  conducted  as  has 
been  described  [page  84]. 

In  these  determinations  Bulb  VI  [page  88]  was  used,  and 
two  new  bulbs,  VII  and  VIII,  for  which  the  following  data 
were  obtained: 

Bulb  VII.  Bulb  VIII. 

P=            4358. 15  gr.  4250. 70  gr. 

p  =                67.17  65.10 

H\  =             753.62  mm.  752.68  mm. 

T\  =               99.76°  99.73° 

Whence  100  6  =                 0.002291  0.002385 

c=                  0.10mm.  0.10mm. 
I  have  brought  together  in  a  single  table  the  results  obtained 
by  this  method  with  different  gases. 


108 


EXPANSION     OF     GASES 


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109 


MEMOIKS    ON 

I  shall  add  a  few  words  upon  the  way  in  which  each  gas  was 
prepared. 

1.  Nitrogen. — This  gas  was  obtained  by  removing  the  oxygen 
of  the  air  by  passing  it  through  a  glass  tube  filled  with  copper 
turnings1   heated  to  redness.     This   tube   was  connected  with 
the  tubulure  of  the  pump.     The  bulb  having  been  exhausted, 
the  tap  is  opened  little  by  little;  the  air  in  passing  over  the  hot 
copper  loses  its  oxygen  and,  later,  gives  up  its  moisture  in  the 
drying  tubes. 

2.  Oxygen. — I  made  many  experiments  upon  oxygen  gas,  but 
they  yielded  figures  so  various  that  it  was  impossible  to  reach 
any  decision  from  them.     Mercury  cannot  be  left  in  contact 
with  oxygen  gas,  even  for  a  very  short  time,  without  absorbing 
a  small  amount  of  the  gas:  its  surface  soon  gives  evidence  of 
mercury  oxide  and  leaves  a  trail  on  the  glass  tube. 

The  same  thing  is  noticed  with  mercury  which  is  left  in  con- 
tact with  the  air,  but  the  change  in  this  case  is  much  slower, 
requiring  a  period  of  several  weeks  to  become  appreciable. 

The  oxygen  was   prepared   by  heating   potassium   chlorate.2 

3.  Hydrogen. — This  gas  was  prepared  by  treating  zinc  with 
dilute  sulphuric  acid  ;  before  entering  the  pump  and  the  dry- 
ing apparatus,  it  was  passed  through  two  tubes,  a  meter  long, 
filled  with  pumice  stone  moistened  with  a  solution  of  caustic 
potash,  and  a  third  tube  filled  with  pumice  stone  moistened 
with  a  solution  of  silver  sulphate.     The  gas  was  entirely  with- 
out odor.     The  introduction  of  the  two  tubes  of  pumice  soaked 
in  a  solution  of  potash  is  chiefly  to  hold  back  the  small  quan- 
tity of  odorous  oily  vapor  which  hydrogen  gas   always  takes 
with  it  and  which  is  sufficient  to  change  appreciably  the  expan- 
sibility of  the  gas.      In  fact,  in   one   experiment  where  the 
hydrogen  gas  passed  merely  through  a  wash  bottle  containing 
water,  I  found  for  its  coefficient  of  expansion  the  figure  0.3686; 

1  The   copper  turnings  were  first  oxidized  by    heating  in  the  pres- 
ence of  air,  then  reduced  by  a  current  of  hydrogen  gas. 

2  Note  by  Translator  :    It  seems  likely  that  Regnault's  oxygen  was 
not  pure — possibly  contained  chlorine,  or  oxides  of  chlorine;  v.  Jolly 
states  that  oxygen  carefully  prepared  from  potassium  chlorate,  or  elec- 
trolytically,  is  entirely  without  action  on  mercury  at  the  temperature  of 
the  experiment. 

110 


EXPANSION    OF    GASES 

a  second  determination  in  which  the  wash  bottle  contained  pot- 
ash-solution, gave  the  figure  0.3679. 

4.  Oxide  of  Carbon. — Prepared  by  decomposing  oxalic  acid 
in  the  presence  of  concentrated  sulphuric  acid:  the  gas  was 
passed  through  a  flask  containing  a  solution  of  caustic  potash 
to  absorb  the  carbonic  acid,  then  through  a  long  tube  filled 
with  pumice  stone  moistened  with  potash  solution;  from  this  it 
passed  into  the  drying  apparatus. 

5.  Carbonic  Acid. — Obtained  by  the  decomposition  of  white 
marble  with  dilute  hydrochloric  acid.     The  gas  passed  through 
a  wash  bottle  containing  water  and   thence   into   the  drying 
apparatus. 

6.  Cyanogen. — This  gas  was  prepared  through  the  decompo- 
sition by  heat  of  cyanide  of  mercury  contained  in  a  small  glass 
retort;  it  passed  through  a  flask  provided  with  a  safety  tube 
and  filled   with  concentrated  sulphuric  acid,  which  serves  to 
regulate  the  flow  of  the  gas. 

7.  Protoxide  of  Nitrogen. — The  protoxide  of  nitrogen  was 
prepared   by  decomposing   with   the   aid   of  heat   ammonium 
nitrate  contained    in  a  retort.     The  gas,   before  entering  the 
drying  tubes,  passed  through  a  wash  bottle  containing  a  solu- 
tion of  protosulphate  of  iron  [ferrous  sulphate]. 

8.  Sulphurous  Acid. — This  gas  was  prepared  by  heating  mer- 
cury with  concentrated  sulphuric  acid.    The  gas  passed  through 
a  wash  bottle  containing  concentrated  sulphuric  acid,  then  the 
usual  drying  apparatus. 

9.  Hydrochloric  Acid  Gas. — Obtained  by  treating  sea  salt 
with   concentrated   sulphuric   acid;  it  was  passed   through  a 
flask   containing   concentrated   sulphuric  acid,   then  through 
two  tubes  full  of  pumice  stone  soaked  with  sulphuric  acid. 

The  experiments  upon  hydrochloric  acid  gas  present  nothing 
out  of  the  way.  The  mercury  retained  its  brilliant  surface.  I 
cannot  have  entire  confidence,  however,  in  the  results  obtained. 
In  fact,  mercury  is  apparently  not  attacked  by  hydrochlorie 
acid  gas  by  itself,  but  it  is  very  quickly  [attacked]  as  soon  as 
the  gas  is  mixed  with  oxygen.  It  is  conceivable  that  a  few 
thousandths  of  air,  mixed  with  the  hydrochloric  acid  gas 
in  the  bulb,  would  serve  to  bring  about  a  very  perceptible 

111 


MEM  OIKS    ON 

absorption  of  gas  and  in  consequence  to  interfere  with  the 
expansion. 

10.  Ammonia  Gas. — Prepared  by  gently  heating  a  concen- 
trated aqueous  -solution  of  the  gas.  It  passed  through  a 
tube  a  meter  long,  filled  with  caustic  potash  broken  in  small 
pieces. 

Ammonia  gas  yielded  most  various  figures.  The  mercury 
seemed  to  be  greatly  changed  at  the  surface:  it  left  a  trail: 
there  had  evidently  been  an  absorption  of  gas;  but  it  has  been 
impossible  for  me  to  determine  the  chemical  reaction  which 
took  place. 

I  found  in  succession  the  figures  0.370,  0.371,  0.373,  accord- 
ing as  the  gas  had  remained  a  longer  or  shorter  time  in  contact 
with  the  mercury. 

It  will  be  seen  in  the  table  above  that  nitrogen,  hydrogen, 
oxide  of  carbon  have  practically  the  same  coefficient  of 
expansion  as  air,  under  the  conditions  when  the  determina- 
tions were  made,  that  is  to  say,  the  gases  being  under  atmos- 
pheric pressure  when  they  are  at  the  boiling  point  of  water, 
and  under  a  pressure  of  about  550  millimeters  when  they  are  at 
the  melting  point  of  ice. 

Carbonic  acid,  protoxide  of  nitrogen  and  cyanogen,  on  the 
contrary,  show  under  the  same  circumstances  a  greater  coeffi- 
cient of  expansion. 

Sulphurous  acid  gas  gave  figures  a  little  higher  than  those 
obtained  for  the  above  gases;  but  the  difference  is  so  small 
that  one  does  not  know  whether  it  may  not  be  due  to  the  inev- 
itable errors  of  experiment. 

I  do  not  discuss  hydrochloric  acid  gas,  since  I  look  upon  the 
numbers  obtained  for  this  gas  as  doubtful. 

My  experiments  therefore  seem  to  show  that  gases  do  not 
have,  under  the  same  conditions,  exactly  the  same  coefficient  of 
expansion.  This  coefficient  varies  for  the  gases  I  have  exam- 
ined, and  with  the  conditions  under  which  the  determinations 
were  made,  from  0.3665  to  0.3685. 

This  variation  cannot  be  attributed  to  the  fact  that,  at  the 
temperature  of  melting  ice  and  under  a  pressure  of  0.555  m., 
certain  of  these  gases  are  close  to  their  point  of  condensation; 
for  sulphurous  acid  is,  of  all  these  gases,  the  easiest  to  liquefy 


EXPANSION    OF    GASES 


and  yet  its  coefficient  of  expansion  is  smaller  than  that  of  car- 
bonic acid  which  at  0°  is  still  removed  by  more  than  90°  from 
its  condensation  point. 

This  modification,  which  must  be  made  in  one  of  the  most 
beautiful  laws  of  physics,  seemed  to  me  too  important  for  me 
not  to  endeavor  to  support  it  by  other  determinations. 

I  began  by  making  several   experiments  with   Method 
using  exactly  the  same  apparatus  as  had  been  used  for  air. 

For  carbonic  acid  gas  I  obtained  the  following  results: 
First  Half. 


IV, 


H 

T 

t 

H' 

h' 

V 

l+100a 

756.52 

99.87° 

13.4° 

755.47 

200.58 

13.0° 

1.36831 

757.54 

99.91° 

12.9° 

758.02 

202.55 

11.7° 

1.36857 

Second  Half. 


Mean  =  1.36844 


H" 

t" 

H'" 

T" 

h'" 

t?" 

758.47 

11.8° 

758.80 

99.95° 

275.67 

14.8° 

758.47 

11.8° 

759.10 

99.97° 

275.51 

14.1° 

1    lOOa 
1.36846 
1.36866 
Mean  =  1.36856 

These  determinations  give  at  least  nearly  the  same  figure  as 
that  found  by  Method  II. 

An  experiment  made  with  protoxide  of  nitrogen  gave  : 
FIRST  HALF.  SECOND  HALF. 


H  =747.03  mm. 

T  =    99.52  ° 
t  =     4.2° 

£T=  748.08  mm. 
h'=  198.39  mm 
t'=      3.6° 
1+100  a  =      1.36701 


H"=  747.72  mm. 

r=    3.6° 

H"=  748.49  mm. 
T"=  99.57° 
h''==  269. 73  mm. 
£"'=     3.9  ° 
1+100  a  =      1.36797 


Mean  =  1.36749 

The  mean  given  by  the  determinations  described  above  and 
made  by  Method  II,  is  1.36763. 

We  have  seen  that  Method  II  gave  for  the  coefficient  of  expan- 
sion of  sulphurous  acid  a  figure  practically  identical  with  that 
found  for  air.  I  wished  to  find  out  whether  this  coefficient 
would  not  become  larger  when  working  under  greater  pres- 
sures. 

An  experiment  made  with  sulphurous  acid  by  Method  IV, 
gave  : 

113 


MEMOIRS     ON 


FIBST  HALF.  SECOND  HALF. 

H  =  742.08  mm.  H"  =  742.49  mm. 
T=    99.33°  t"  =      5.3° 

t  =      5.6  °  H"'  =  742.85  mm. 

H=  742.31  mm.  T"  =   99.36 

h'=  196.64  mm.  h'"  =  267.64  mm. 

t'=     4.5°  «'"  =     6.6° 
1+100  a  =    1.36689               1-flOO  a  =    1.36777 

The  figure  obtained  in  the  first  half  of  the  determination  is 
identical  with  that  found  in  the  experiments  made  by  Method 
II,  whereas  that  given  by  the  second  half,  that  is,  under 
greater  pressures,  is  notably  greater. 

A  second  trial  was  made  by  subjecting  the  sulphurous  acid  to 
a  little  more  than  atmospheric  pressure  when  the  gas  was  at 
0°.  The  bulb  was  surrounded  with  ice  and  the  side  tube  put 
in  communication  with  the  apparatus  generating  sulphurous 
acid  gas,  when  the  mercury  was  run  out  by  opening  the  tap, 
so  as  to  let  the  tube  FH  become  entirely  filled  with  sulphurous 
acid  gas.  The  tubej9  was  then  sealed  with  a  lamp.  Mercury 
was  poured  into  the  tube  G,  so  as  to  bring  the  level  to  a  in  the 
tube  FH.  A  difference  of  level  h  is  then  noted  between 
the  two  menisci.  The  ice  was  removed  and  the  bulb  raised  to 
the  boiling  point  of  water,  as  in  the  ordinary  determinations. 
We  thus  have  : 

H 743.59mm. 

t   5.6°- 

h    28.69mm. 

H 743.92mm. 

T1 99.40° 

h' 308.22mm. 

t 6.1° 

1+100  a 1.36907 

Finally,  a  third  determination  was  made  subjecting  the  gas 
to  a  much  higher  pressure  still.  For  this  the  tube  FH  was 
replaced  by  another,  the  lower  part  of  which  had  a  much 
greater  volume.  This  tube  is  shown  in  Fig.  15  [page  101]. 

Working  exactly  as  in  the  second  determination,  we  find  : 

114 


EXPANSION     OF     GASES 

H  =  764.77  mm.  H'  =  764.64  mm. 

t  =      5.9  °  T'  =  100.17 

h  =  136.29  mm.  h'  =  469.71  mm. 

t'=    7.00° 

_H_  =.00336 
V 

whence 

l+100a  =  1,37413. 

Thus  for  sulphurous  acid  the  results  are  : 

The  gas  at  0°  under        At  100°  under 
a  pressure  of  a  pressure  of 

545.67mm.  742.08mm.  1J 

742.49  1010.49  1.36777 

772.28  1052.14  1.36907 

901.06  1234.35  1.37413 

The  coefficient  of  expansion  of  sulphurous  acid  therefore 
increases  in  a  very  marked  way  in  proportion  as  the  pressure  to 
which  the  gas  is  subjected  becomes  greater.  It  is  probable  that 
the  same  thing  takes  place  in  all  compound  gases  for  which  the 
law  of  volumes  does  not  rigorously  hold  or  which  do  not  exactly 
follow  Mariotte's  Law. 

A  similar  variation  is  to  be  noticed  in  carbonic  acid  gas, 
although  in  a  much  less  decided  way.  We  have  seen  that 
Method  IV,  applied  to  this  gas,  gave  : 

Pressure  at  0°  At  100  ° 

554.89  mm.  756.52  mm.  1.36831 

555.47  757.54  1.36857 

758.47  1034.47  1.36846 

759.10  1034.61  1.36866 

The  difference  is  not  noteworthy.  But  an  experiment  made 
with  the  modified  apparatus  which  I  have  described,  gave  : 

H  =  766.32  mm.  H1  =  766.14  mm. 

t    =     6.4°  T'  =  100.23° 

h  =  134.77  mm.  t1  =      6.4° 

h<  =  464.23  mm. 
v 
-y-  =  0.00336. 

1  +  100  a    =1.36943. 
115 


MEMOIRS     ON 


Thus,  at  0°  under  a  pressure  of  901.09  mm.  and  at  100° 
under  a  pressure  of  1230.37,  the  coefficient  of  expansion  of  car- 
bonic acid  gas  is  distinctly  higher. 

I  have  constructed  an  apparatus  by  means  of  which  one  may 
at  once  detect  unequal  expansion  in  gases  and  which  may  serve 
to  measure  this  difference  with  accuracy.  This  apparatus, 
which  is  a  kind  of  differential  thermometer,  consists  of  two 
bulbs  of  equal  capacity,  complete  with  capillary  tubes  and 
arranged  exactly  like  the  bulb  of  Method  IV  (Fig.  13),  [page 
96].  Each  of  these  bulbs  connects  with  a  tube  similar  to  the 
tube  FH  of  Figs.  13  and  14,  cemented  into  a  three-way  tube 
of  iron  provided  with  a  tap,  Fig.  16.  The  third  branch,  in  the 
middle,  holds  a  piece  of  barometer  tubing.  The 
two  tubes  FGH  and  F'GH'  were  cut  from  the 
same  accurately  cylindrical  piece  of  tubing  and 
have  exactly  the  same  shape  ;  they  are  fixed  as 
alike  as  possible  in  the  tubulures.  One  of  the 
bulbs  is  filled  with  dry  air  and  the  other  with  the 
gas  whose  expansibility  it  is  desired  to  compare 
with  that  of  air.  Moreover,  the  bulbs  are  fast- 
ened in  the  same  tin  vessel. 

The  bulbs  being  surrounded  with  melting  ice, 
and   the    mercury   having  been  adjusted  to  the 
Cf\         YG'      level  of  a  mark  scratched  on  one  of  the   tubes, 
the  two  side  tubes   op  are   closed   with   a   lamp. 
The  mercury  is  then  of  necessity  at  the  same  level 
in  the  two  tubes  FGHand  F'G'H'  and  in  the  up- 
right tube  between  them.     The  ice  having  been 
removed    and    water   put  in  the  tin  vessel,  the 
latter    is    brought    to   boiling  while  mercury  is 
1|)K-         poured  into  the  intermediate  tube  to   keep   the 
FIG.  16.          level  at  the  same  point    in  the  tube  FGH.     If 
the  two  gases  have  the  same  coefficient  of  expansion,  the  two 
menisci    in  the  tubes  FGH  and  F'G'H'  will  be  at  the  same 
level ;  there  will  be  a  difference  of  level,  on  the  other  hand,   if 
the  [rates  of]  expansion  are  unequal. 

It  would  be  very  difficult  to  find  two  bulbs  of  exactly  the 
same  capacity  when  they  are  sealed  to  their  capillary  tubes, 

116 


EXPANSION    OF    GASES 

and  also  so  to  arrange  the  tubes  FGH  and  F'G'H1  that  the  vol- 
ume of  air  contained  in  the  upper  part'of  these  tubes  should  be 
exactly  equal  when  the  mercury  is  at  the  same  level  and 
adjusted  to  the  mark  made  on  one  of  them.  Yet  this  is  not 
necessary  ;  it  will,  in  fact,  serve  if  the  ratio  -^-  is  the  same  for 
the  two  pieces  of  apparatus.  It  will  do,  indeed,  for  this  to 
take  two  bulbs  of  nearly  the  same  volume  and  gauge  them 
carefully  by  means  of  distilled  water,  after  they  have  been 
attached  to  their  capillary  tubes.  In  the  same  way  the  tiny 
volume  in  the  part  Fa  of  the  tube  FGH  us  far  as  the  mark  a, 
is  measured  by  means  of  mercury;  on  the  other  tube  F'G'H'  are 
made  two  marks,  a'  and  a",  and  the  volume  up  to  a"  and  that 
between  the  two  marks  a  and  a",  are  calibrated  by  means  of 
mercury. 

This  done,  we  know  the  ratio  ^  for  the  first  bulb,  and  the 
volume  V'  of  the  second  bulb;  then  v1  must  be  equal  to 
-2=>  V.  It  is  easy  to  find  the  point  on  the  tube  G'  Hf  which 
corresponds  to  this  volume  v'  ;  its  distance  d  from  the  mark  a< 
is  then  calculated. 

The  tube  FGH  being  cemented  in  its  tubulure  and  the 
apparatus  fastened  to  its  vertical  support,  the  tube  F'G'H1  is 
fixed  in  the  place  where  it  belongs.  For  this  purpose,  the  level 
of  the  mark  a  upon  the  tube  FGH  is  found  with  the  cathetom- 
eter,  and  the  glass  is  then  turned  towards  the  tube  F'G'H1. 
If  the  latter  tube  is  in  the  proper  position,  the  crossing  of  the 
threads  of  the  glass  should  be  aiming  at  the  point  which  cor- 
responds to  the  volume  V1;  consequently  the  mark  a!  should  be 
at  a  distance  d  above  or  below  ;  by  means  of  the  instrument  we 
find  whether  this  is  in  fact  the  case,  that  is,  the  glass  is  raised 
or  lowered  by  an  amount  d,  and  the  tube  F'G'H'  is  adjusted  so 
that  the  mark  a'  is  hidden  by  the  horizontal  thread  of  the  glass 
in  its  new  position  ;  then  the  tube  is  fastened  in  place  with 
mastic. 

To  make  sure  that  the  differential  apparatus  is  properly 
adjusted,  an  experiment  is  made,  filling  both  bulbs  with  dry 
air.  The  two  side  tubes  op  are  closed  when  the  bulbs  are  in 
melting  ice  and  the  mercury  has  been  brought  to  the  level  of  a 

117 


MEM  OIKS     ON 

in  the  tube  FGH.  The  three  columns  of  mercury  are  then  at 
the  same  level.  Water  is  then  put  in  the  boiler  and  the  level 
of  the  mercury  is  kept  at  a;  the  mercury  must  be  at  exactly  the 
same  height  in  F'G'ff'  if  the  apparatus  is  properly  put  together. 

The  results  reached  by  this  method  are  rendered  still  more 
certain  by  performing  a  second  experiment  in  which  the  gas 
whose  expansibility  we  wish  to  determine,  is  introduced  into 
the  bulb  which  has  hitherto  held  the  air,  while,  on  the  other 
hand,  atmospheric  air  is  put  in  the  bulb  which  in  the  former 
experiment  contained  the  gas. 

The  equation  which  gives  the  expansibility  of  the  gas  in  the 
case  of  this  apparatus  is  clearly 


the  symbols  having  the  same  meaning  as  on  page  100. 

If  we  diiferentiate  with  respect  to  a  and  Ji"1,  bearing  in  mind 

that  the  factor^-—  5_  (ff"f  +  h'l(  —  H")  is  very  small  and  may 
be  supposed  contant  and  equal  to  &,  we  have 


we  can  then  write  it  simply 

»-££ 

That  is,  the  difference  in  the  coefficients  of  expansion  of  the 
two  gases  is  equal  to  the  difference  in  the  levels  of  the  columns 
of  mercury  in  the  two  tubes  FGH  and.  F'G'H',  divided  by  the 
barometric  height  at  the  time  the  two  tubes  were  sealed  when 
the  bulbs  were  in  melting  ice. 

This  result  is  not  however  altogether  accurate,  since  we  have 

taken  no  account  of  the  variation  of  the  ratio  ^  —  which  is 
not  the  same  at  100°  as  at  0°  —  for  the  gas  which  does  not 
expand  at  the  same  rate  as  air.  But  when  the  difference  in  the 
ratio  of  expansion  is  very  slight,  the  error  introduced  by  this 
omission  is  practically  inappreciable.  On  the  other  hand,  it  is 
easy  to  take  it  into  account. 

118 


EXPANSION    OF     GASES 

A  test  determination  made  by  this  method  with  carbonic  acid 
gas  and  atmospheric  air,  gave 

A  h"'  =  1.48  mm.,  //"  =  757.20; 
hence 

A  a  =  '757™™'  =  0.002  (about) ; 

that  is,  the  coefficient  of  expansion  of  carbonic  acid  gas  is  0.002 
higher  than  that  of  air — which  gives  0.3685;  and  this,  in  fact, 
is  the  figure  which  we  found  above  [page  113]. 

To  prove  the  accuracy  of  the  differential  apparatus,  I  filled 
both  bulbs  with  dry  air;  I  then  found 
A  h'"  =  0.08  mm. 

This  difference  is  probably  due  to  the  fact  that  the  tubes 
were  not  quite  perfectly  adjusted,  but  it  is  entirely  inappreci- 
able. 


119 


EXPANSION    OF    GASES 


BIOGRAPHICAL  SKETCH. 

Henri  Victor  Eegnanlt  was  born  at  Aix  la  Chapelle  in  the 
year  1810,  July  21.  He  was  educated  at  the  Ecole  Poly  tech- 
nique and  the  Ecole  des  Mines.  He  became  Gay-Lussac's  suc- 
cessor as  Professor  of  Chemistry  in  the  former  institution  in 
1840,  and,  the  next  year,  Professor  of  Physics  in  the  College  de 
France.  Up  to  this  time  his  researches  were  confined  to 
organic  chemistry:  an  important  paper  on  the  ethers  appeared 
in  1835.  From  1847  to  1854  he  was  Chief  Engineer  of  Mines, 
and  subsequently  became  director  of  the  famous  porcelain 
works  at  Sevres.  From  1841,  for  over  twenty  years,  he  published 
the  results  of  research  after  research  upon  the  physical  con- 
stants of  gases,  of  liquids  and  of  solids.  In  this  extraordinary 
series  are  to  be  found  investigations  of  the  compressibility  of 
gases,  liquids  and  solids;  of  their  densities,  and  rates  of  expan- 
sion; of  the  tension  of  vapors;  of  calorimetrical  methods;  of 
the  latent  heat  of  substances;  of  their  specific  heat,  etc.,  etc. 
In  addition,  may  be  mentioned  contributions  to  the  mechanical 
theory  of  heat  and  study  of  the  velocity  of  sound.  All  the 
records  of  his  latest  work  were,  to  his  great  sorrow  and  to 
the  loss  of  the  scientific  world,  destroyed  during  the  Franco- 
Prussian  War.  His  scientific  labors  ended  in  1872,  but  he 
lived  until  Jan.  19,  1878.  Regnault's  great  reputation  rests 
upon  his  extraordinary  skill  in  devising  and  using  apparatus. 
It  may  be  said  that  in  whatever  direction  his  researches  led 
him,  he  invariably  succeeded  in  discovering  sources  of  error  in 
the  work  of  his  predecessors  and  in  eliminating  it,  at  least  in 
large  measure,  from  his  own  results. 


120 


RESEARCHES  UPON  THE  EXPANSION 

OF  GASES. 

BY  HESTRI  VICTOR  EEGNAULT. 
Second  Memoir. 


121 


CONTENTS. 

PAGE 

Object     .         .        .        .         .         .         .                 .         .  123 

Experiments  under  pressures  less  than  the  atmospheric: 

Method 124 

Results 126 

Experiments  under  pressures  greater  than  the  atmospheric: 

Method 127 

Apparatus 127 

Results 134 

Application  of  method  to  Carbon  dioxide       .        .136 

Expansion  of  Gases  under  Constant  Pressure: 

Importance  of  research 136 

Apparatus  and  manipulation        ....  138 
Results  ivith  air    .        .        .        .        .         ,        .143 

Results  with  hydrogen 143 

Results  with  other  gases        .....  143 

Errors  discovered  in  results  of  First  Memoir      .        .         .  145 

Comparison    of    results,   constant   volume    and   constant 

pressure 148 

Conclusions .  150 


122 


RESEARCHES  UPON  THE  EXPANSION 

OF  GASES. 

BY  M.VICTOR  REGKAULT. 
Second  Memoir. 

IK  a  former  treatise  (Annales  de  Ghimie  et  de  Physique,  3d 
Series,  volume  IV,  page  5),  I  discussed  the  determination  of 
the  coefficients  of  expansion  of  air  and  of  some  other  gases 
between  the  fixed  points  of  the  thermometer  and  under  pres- 
sures little  removed  from  that  of  the  atmosphere.  The  various 
methods  of  experimentation  employed,  speaking  generally,  show 
one  point  in  common:  the  expansions  were  not  measured 
directly,  but  were  calculated  from  the  changes  in  the  tension. 
In  this  second  memoir  I  propose: 

I.  To  complete  the  earlier  researches  and  to  study  the  rate 
of  expansion  of  gases  between  the  same  limits  of  temperature 
but   under   very   diverse   pressures,  by   the   use   of  analogous 
methods,  that  is,  those  based  upon  the  measurement  of  the 
variations  of  the  tension  which  a  given  volume  of  gas  shows 
when  its  temperature  rises  from  0°  to  100°; 

II.  To  examine  the  same  subject  in  a  direct  way  by   an 
entirely  different  method,  in  which  we  measure  at  once  the 
increase  of  volume  which  a  rise  of  temperature  from  0°  to  100° 
produces  in  a  given  quantity  of  gas  subjected  all   the  time  to 
the  same  pressure. 

FIRST  PART. 

On  the  Rate  of  Expansion  of  Gases  under  Various  Pressures, 

Calculated  from  the  Changes  in  the  Tension. 
Physicists  generally  assume  that  the  rate  of  expansion  of 
gases  is  constant  between  the  limits  of  temperature  mentioned, 
whatever  the  pressure  to  which  the  gases  are  subjected  ;  con- 
sequently, that  it  is  entirely  independent  of  the  original  den- 
sity of  the  gas.  Yet  it  is  difficult  to  cite  any  conclusive 
experiments  upon  which  this  law  may  be  based.  Many  observers 

123 


MEMOIRS    ON 

have  obtained  the  same  figure  for  the  coefficient  of  expansion 
of  air  under  various  barometric  pressures,  and  have  from  this 
fact  concluded  that  the  coefficient  of  expansion  of  gases  remains 
constant  under  all  pressures.  Yet  the  barometric  variations  in 
any  given  place  are  within  limits  too  narrow  to  permit  of  draw- 
ing so  general  a  conclusion  from  such  observations  ;  they  only 
prove  that,  for  slight  variations  of  pressure,  the  changes  in  the 
coefficient  of  expansion  of  air  are  inappreciable. 

H.  Davy  is  the  only  physicist  who  has  studied  the  expansi- 
bility of  gases  under  very  varied  pressures  (Philosophical  Trans- 
actions, 1823,  volume  II,  page  204).  He  states  that  he  found 
the  expansion  for  air  at  the  densities  £,  J,  £,  1  and  2.  Yet  the 
determinations  were  not  made  by  a  method  exact  enough  for 
us  to  consider  their  results  as  sufficiently  accurate. 

I  have  made  experiments  upon  air  under  pressures  much 
lower  than  that  of  the  atmosphere  and,  again,  others  under 
pressures  far  greater. 

Experiments  under  Pressures  less  than  the  ordinary 
Barometric  Pressure. 

These  determinations  were  carried  out  by  Method  IV 
(Annales  de  Chimie,  volume  IV,  page  38  [above,  page  96]  ),  and 
by  means  of  the  apparatus  shown  in  Figs.  13  and  14  [page  96] ; 
greater  length,  however,  is  given  the  tube  /Yr/f— about  770 
millimeters  from  the  tubulure  H  up  to  the  mark  a.  After 
placing  the  bulb  in  the  vapor  of  boiling  water  and  connecting 
it,  on  the  one  hand,  with  the  drying  apparatus  by  means  of  the 
side  tube  op  and,  on  the  other,  with  the  tube  FGH  which  is 
cemented  with  mastic  into  its  copper  tubulure  n,  it  is  exhausted 
a  great  many  times,  and  the  air  allowed  each  time  to  enter 
again  very  slowly  :  the  tubes  FH  and  //contain  enough  mer- 
cury for  a  vacuum  to  be  produced  in  the  bulb  without  the 
mercury  rising  above  Fin  the  tube  FH.  When  the  apparatus 
is  completely  dried  out,  the  amount  of  air  we  wish  to  experi- 
ment with  is  admitted  ;  its  density  being  determined  by  the 
difference  of  level  of  the  two  columns  of  mercury.  The  side 
tube  op  is  then  sealed  with  a  lamp  and  the  drying  apparatus 
removed. 

By  pouring  mercury  into  the  tube  //,  the  level  in  the  tube 
FH  is  adjusted  at  the  mark  a, -the  bulb  being  all  the 'time  in 

124 


EXPANSION    OF    GASES 

the  vapor  of  boiling  water  ;  by  means  of  the  cathetometer  the 
difference  of  level  of  the  two  columns  is  read,  and  at  the  same 
time  the  barometric  height  is  recorded. 

The  furnace  0  is  then  removed,  the  hot  water  in  the  vessel 
Jfis  drawn  off  and,  when  the  latter  has  become  quite  cold,  the 
bulb  A  is  surrounded  with  crushed  ice.  Mercury  is  drawn  off 
by  opening  the  tap  K  so  as  to  maintain  the  mercury  level  at 
the  point  a  in  the  tube  FH.  When  temperature  equilibrium 
has  once  more  been  established,  the  difference  of  level  of  the 
mercury  columns  is  measured,  as  well  as  the  barometric  height. 

Several  determinations  were  thus  made  with  the  same  speci- 
men of  air,  having  the  bulb  successively  in  the  vapor  of  boil- 
ing water  and  in  melting  ice.  They  were  performed  in  some 
cases  after  several  days'  interval  ;  in  this  way  it  was  easy  to 
decide  whether  the  apparatus  was  perfectly  gas-tight. 

I  have  brought  together  in  a  single  table  the  determinations 
made  of  the  rate  of  expansion  of  air  under  pressures  lower  than 
that  of  the  atmosphere  ;  those  that  were  made  upon  the  same 
specimen  of  air  are  comprised  in  a  single  series. 

I  used  the  same  bulb  as  in  my  earlier  experiments  (volume 
IV,  page  42  [page  88,  above]  ),  but  the  tube  FH  of  the  old 
apparatus  was  replaced  in  Experiments  II,  III,  IV,  and  V,  by 
another  of  greater  height. 

For  Series  I,  we  have 

JL==26.85_         OQ27 
V       9889.9  ~ 
and  for  Series  II,  III,  IV  and  V, 

V=  9889.  9  ==0'00298- 

The  formula  which  serves  for  the  calculation  of  the  experi- 
ment is  the  following  : 

Representing  by  H1  the  barometric  height  at  the  time  when 
the  experiment  is  carried  out  in  [the  vapor  of]  boiling  water, 

T  the  temperature  of  the  vapor, 

lil  the  difference  of  level  of  the  mercury  columns, 

tl  the  temperature  of  the  minute  air-volume  v, 

H,  h,  t,  the  corresponding  quantities  when  the  experiment 
is  conducted  in  melting  ice  ; 

We  then  have  : 


-*)-£  —I—  tlH>-h>-H+h] 
125 


MEMOIKS     ON 


We  have  assumed  that  t1  =  t. 

The  heights  H,  h,  ff,  lil  have  been  reduced  to  0°  by  calcula- 
tion. 

In  the  calculation  of  the  determinations  the  same  figure  for 
melting  ice  has  been  combined  with  several  results  for  boiling 
water,  made  before  and  after,  to  eliminate  the  extreme  values. 

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ab 


EXPANSION    OF    GASES 

This  table  shows  clearly  that  the  coefficient  of  expansion  of 
air  continues  to  decrease  with  the  pressure. 

It  is  noteworthy  that,  in  the  several  experiments  made  upon 
the  same  specimen  of  air,  greater  variations  are  recorded  than 
in  those  made  under  atmospheric  pressure.  Thus,  in  Series  V, 
which  comprises  determinations  made  under  very  low  pressures, 
the  extremes  are  1.36376  and  1.36639  ;  difference,  0.00263. 
The  reason  for  this  is  simple  ;  the  same  error  made  in  the 
reading  of  one  of  the  heights  H,  H',  h,  or  h',  of  necessity  pro- 
duces much  more  considerable  variations  in  the  final  result,  the 
lower  the  pressures.  It  is  only  by  a  great  many  determinations 
arranged  so  as  to  eliminate  extreme  figures,  and  by  taking  into 
account  all  results  that  were  obtained,  that  it  has  been  possible 
to  prove  the  existence  of  the  law  stated  above. 

Experiments  under  Pressures  greater  than  the  ordinary 
Barometric  Pressure. 

The  apparatus  [shown  in]  Volume  IV,  Fig.  13  and  14  [page 
96]  serves  very  well  for  experiments  under  pressures  higher 
than  the  atmospheric,  when  modified  as  follows: 

The  tube  //  is  replaced  by  a  much  longer  glass  tube  held 
fast  to  a  wall  by  numerous  supports  throughout  its  length. 
Instead  of  the  straight  side  tube  op,  there  is  cemented  into  the 
tubulure  o  a  tube  of  the  form  shown  in  Fig.  1  and  consisting  of 
a  bent  capillary  tube  abc  of  which  the  portion  ab  is  horizontal, 
and  of  a  larger  tube  cd  sealed  to  the  capillary  tubing  and  verti- 
cal in  position.  The  latter  connects  with  a  large  tube  LL' 
containing  pumice  stone  moistened  with  concentrated  sulphuric 
acid:  for  this  purpose,  the  ends  of  the  two  tubes  are  brought 
together  inside  the  little  cover  tube  of  copper  which  is  then 
covered  all  over  with  gum  mastic.  The  tube  LL'  can  be  con- 
nected by  means  of  a  rubber  tube  with  a  small  air  pump  or 
cemented  into  the  tubulure  t  of  a  condensing  pump. 

A  number  of  pellets  of  gum  mastic  are  put  in  the  tube  cd. 

This  being  arranged  and  the  bulb  being  in  the  vapor  of  boil- 
ing water,  the  apparatus  is  exhausted  many  times  for  the  pur- 
pose of  drying  it  completely,  then  the  vacuum  pump  is  replaced 
by  the  condensing  pump;  dry  air  is  slowly  forced  into  the  bulb 

127 


MEMOIRS    OK 

and,  at  the  same  time,  mercury  is  poured  into  the  tube  IJ. 
Some  minutes  are  allowed  to  elapse  between  consecutive  strokes 
of  the  piston,  in  order  to  let  the  air  remain  some  time  in  con- 
tact with  the  sulphuric  acid  in  the  pumice  stone  before  it 
makes  its  way  into  the  bulb.1  When  it  is  seen  by  the  difference 


FIG.  1. 


FIG.  2. 


of  height  of  the  mercury  columns,  that  the  air  in  the  bulb  is 
at  the  desired  density,  the  small  pellets  of  gum  mastic  con- 
tained in  the  tube  cd  are  melted  with  the  aid  of  an  alcohol 
lamp,  and  at  the  same  time  the  tap  K  is  opened  a  little;  the 

1  It  is  even  more  necessary  in  the  case  of  determinations  made  under 
high  pressures  than  of  those  under  low,  that  the  air  admitted  to  the 
bulb  should  be  perfectly  dry.  To  secure  this  result  to  a  certainty,  care 
is  taken  to  fit  a  second  tube  of  pumice  stone  and  sulphuric  acid  to  the 
tubulure  t'  of  the  condensing:  pump,  so  that  the  air  introduced  comes 
iato  the  pump  already  well  dried. 

128 


EXPANSION     OF     GASES 

mercury  which  runs  out  lowers  the  tension  within  enough  to 
cause  a  short  column  of  melted  gum  mastic  to  make  its  way 
into  the  capillary  tube  cb,  where  it  solidifies.  The  same  end  is 
manifestly  reached  by  forcing  in  more  air  by  means  of  the 
condensing  pump.  The  apparatus  is  now  hermetically  sealed 
at  c,  when  the  gum  mastic  becomes  cold;  the  tube  LL  and 
the  condensing  pump  can  then  be  removed. 

The  determination  proceeds  as  usual;  only,  since  the  col- 
umns to  be  measured  are  very  long,  they  cannot  be  brought 
within  the  range  of  a  single  cathetometer.  I  have  therefore 
used  in  these  experiments  two  eathetolneters  at  one  time,  each 
of  1  meter's  range.  One  of  these  instruments  served  to  deter- 
mine the  distance  of  the  meniscus  in  the  tube  FH  down  from 
a  mark  r  made  upon  the  tube  IJ  at  about  800  millimeters 
above  the  mark  a.  The  other  cathetometer,  fixed  upon  a  very 
steady  base  which  the  observer  does  not  touch,  serves  to  mea- 
sure the  distance  from  the  meniscus  in  the  tube  //  down  to 
another  mark  r'  made  upon  this  same  tube.  When  the 
distance  rr  is  greater  than  1  meter,  other  marks  are  put 
upon  the  same  tube  in  the  interval,  separated  by  about  900 
millimeters.  All  these  distances  were  each  time  determined 
with  the  greatest  care  by  means  of  cathometers,  before  the 
experiment  was  begun  and  again  after  it  was  finished. 

The  meniscus,  in  the  tube  FH  was  adjusted  in  each  experi- 
ment approximately  to  coincide  with  the  mark  a  on  the  tube: 
since  it  is  rather  difficult  to  adjust  such  long  columns  of  mer- 
cury, I  did  not  attempt  each  time  to  make  the  coincidence 
perfect;  I  preferred  to  secure  it  only  approximately  and 
to  take  account  of  the  variation  in  the  minute  volume  v, 
from  the  position  of  the  meniscus  with  respect  to  the 
mark  a, — which  was  made  easy  by  a  previous  calibration  of  the 
tube. 

The  mercury  column  was  protected  from  radiated  heat  by  a 
wall  of  several  planks  on  top  of  one  another:  the  tempera- 
ture was  determined  by  means  of  three  thermometers  with  very 
large  bulbs,  placed  at  different  points  along  its  length.  The 
mean  of  the  readings  of  these  thermometers  was  taken  as  the 
temperature  of  the  mercury  column. 

By  means  of  the  apparatus  thus  arranged  I  was  able  to 

129 


MEMOIRS    ON 

make  determinations  up  to  a  pressure  of  about  four  atmos- 
pheres. The  bulb  was  no  longer  that  which  had  served  for 
the  previous  experiments;  that  was  of  too  thin  glass  and 
probably  would-  not  have  withstood  so  great  a  pressure.  I 
chose  a  thicker  glass  bulb  and  one  of  somewhat  smaller  diame- 
ter; it  held  6786.5  grams  of  mercury  at  0°. 

In  order  to  make  observations  at  yet  higher  pressures,  I  was 
compelled  to  resort  to  a  new  arrangement.  I  was  unable  to 
procure  glass  tubing  in  single  pieces  of  more  than  three  meters 
in  length,  and  moreover  I  was  afraid  that  a  glass  tube  of 
greater  dimensions  would  not  withstand  the  pressure  and  would 
give  way  at  the  lower  end.  I  had  recourse  to  the  following 
apparatus  (Fig.  1)  [page  128]: 

An  iron  tube,  about  three  meters  in  length,  is  fitted  into  the 
tubulure  A  of  an  iron  vessel  provided  with  a  tap  (Fig.  1,  2);1 
it  is  fastened  in  this  tubulure  by  means  of  a  packing  of  linen 
greased  with  tallow,  which  is  forced  into  the  annular  space 
around  the  tube  by  means  of  the  screw  cap  E. 

In  the  second  tubulure  B  is  fixed  in  the  same  way  the  glass 
tube  FH.  The  iron  vessel  ABR  is  firmly  fastened  by  a  sup- 
port 88'  fixed  upon  a  vertical  wall.  The  iron  tube  is  arranged 
exactly  vertical ;  its  upper  end  is  made  wider  and  is  provided 
with  a  screw-thread,  and  in  this  is  fitted  a  glass  tube  about  2 
meters  in  length  with  the  aid  of  a  packing  of  linen  greased  with 
tallow  and  a  screw  cap.  The  iron  tube  and  the  glass  tubing 
which  it  carries  have  an  interior  diameter  of  14  to  15  milli- 
meters. 

The  bulb  with  the  vessel  that  contains  it  is  placed  in  a 
neighboring  room,  separated  from  the  first  by  the  wall  upon 
which  the  vertical  iron  tube  is  fastened.  This  wall  is  pierced 
with  a  hole  through  which  the  capillary  tube  of  the  bulb  is 
passed  before  it  is  cemented  into  the  copper  three-way  tube 
mno.  The  side  tube  mo  carries  a  small  bent  tube  abed  contain- 
ing pellets  of  gum-mastic,  and  is  connected  with  the  condens- 


1  "Fig.  2  shows  a  vertical  section  of  the  vessel  ABR  on  a  scale  double 
that  of  Fig.  1.  All  the  figures  are  -fa  actual  size,  except  Fig.  2  and  4  of 
this  memoir  [see  page  138]  which  are  £  actual  size. 

130 


EXPANSION     OF    GASES 

ing  pump  by  means   of   the   tube    LL   full  of   pumice  stone 
moistened  with  sulphuric  acid. 

The  determination  is  in  other  respects  carried  out  exactly  as 
with  the  former  apparatus:  the  two  menisci  are  followed  with 
two  cathetometers.  The  instrument  which  follows  the  menis- 
cus of  the  long  column  is  placed  on  an  upper  floor,  through  the 
planking  of  which  the  iron  tube  passes. 

The  tubes  bear  marks  at  chosen  distances  which  have  been 
measured  with  the  greatest  care  by  means  of  one  of  the  cathetom- 
eters placed  for  this  purpose  upon  high  supports  made  as  firm 
as  possible  and  upon  which  the  observer  doos  not  rest.  The 
very  sensitive  spirit  level  of  the  cathetometer,  moreover,  en- 
ables one  easily  to  judge  if  the  condition  of  steadiness  is  satis- 
factorily secured. 

Mercury  thermometers  with  large  bulbs  are  arranged  along 
the  mercury  column  and  indicate  its  temperature. 

The  bulb  used  in  these  determinations  was  one  of  thick  glass 
which  I  had  blown  for  me  at  the  glass  works  of  Choisy-le-Roi. 
The  walls  of  the  bulb  were  about  3  millimeters  thick  and  were 
practically  uniform  throughout.  The  coefficient  of  expansion 
of  this  bulb  was  determined  from  another  smaller  one,  blown 
at  the  same  time,  of  the  same  material,  and  having  almost  the 
same  thickness  of  glass;  it  was  found  to  be  0.002130  between 
0°  and  100°. 1 

The  bulb  used  in  the  experiments  on  the  rate  of  expansion 
of  gases  held  5864.45  gr.  of  mercury  at  0°,  apart  from  the 
capillary  stem. 

Finally,  there  is  a  factor  which  we  must  know  in  order  to  be 
able  to  calculate  the  rate  of  expansion  of  air  from  the  results  of 
experiment:  this  is  the  increase  in  the  capacity  of  the  bulb 
through  the  variation  in  the  pressure  upon  the  gas  at  0°  and  at 
100°.  This  variation  would  be  difficult  to  determine  perfectly 
accurately,  but  it  is  easy  to  obtain  an  approximate  figure. 

To  this  end  the  bulb  was  filled  with  water  to  within  a  short  dis- 
tance from  the  end  of  the  capillary  stem,  and  this  end  was  then 


1  The  data  of  this  determination  are  the  following: 

P  =  1265.647  gr.  Hi  =  763.50  mm. 

p  =      19.783  n=100.13° 

131 


MEMOIRS     ON 

cemented  into  a  bent  glass  tube  whose  long  vertical  arm  was 
open.  If  it  was  desired  to  determine  the  changes  of  volume 
for  slight  pressures,  mercury  was  poured  into  the  open  end: 
the  air  compressed  in  the  other  arm  exerts  pressure  upon  the 
water  surface  in  the  capillary  tube.  The  increase  in  the  capac- 
ity of  the  bulb  is  gauged  by  the  movement  of  the  water  menis- 
cus in  the  capillary  tube,  and  the  pressure  by  the  difference  of 
level  of  the  mercury  columns.  The  bulb  was  immersed  in  a 
vessel  of  water  at  the  ordinary  temperature,  to  render  inappre- 
ciable the  volume-changes  due  to  variations  of  temperature. 

Below  are  some  data  obtained  with  the  bulb  which  was  used 
in  the  determinations  of  page  56  [page  126]  and  in  those  of 
the  former  memoir,  page  42,  volume  IV  [page  88]  : 

Under  a  pressure  of  The  capacity  increased  by 

227.7  mm.  of  mercury  0.000054 
436.5          "  0.000103 

687.8  "  0.000160 

Evidently  the  capacity  increases  with  the  pressure;  yet  this 
increase  of  volume  is  so  slight  that  it  may  be  completely  neg- 
lected in  experiments  made  upon  the  expansibility  of  gases 
under  atmospheric  pressure.  The  change  in  the  capacity  of 
the  bulb  is  actually  still  less  than  is  here  indicated,  for  in  the 
experiment  described  the  apparent  change  was  composed  not 
only  of  the  increase  in  the  volume  of  the  glass  bulb,  but  also 
of  the  decrease  in  volume  of  the  water;  I  have  entirely  neg- 
lected the  latter  and  have  ascribed  the  whole  change  observed 
to  the  variation  in  the  bulb's  capacity. 

For  studying  the  increase  in  the  volume  of  the  bulb  under 
higher  pressures,  I  sealed  a  capillary  tube  of  rather  large  bore 
to  a  thick  glass  bulb  similar  to  that  of  the  experiments  described 
on  page  61  [page  131].  This  bulb  was  completely  filled  with 
water  and  connected  with  a  condensing  pump  and  a  small  air- 
manometer;  in  this  way  I  obtained  the  following  results: 

Under  an  increase  of  The  volume          Under  an  increase  of  pressure 

pressure  of  changed  by  of  1  meter  [of  mercury] 

0.715  m.  0.0000740  0.0001035 

1.814  0.0001940  0.0001069 

3.035  0.0003288  0.0001083 

4.178  0.0004538  0.0001086 

132 


EXPANSION    OF    GASES 

We  shall  assume  0.000108  [to  be  the  increase  produced]  by 
a  rise  in  pressure  of  1  m.  of  mercury. 

To  obtain  the  increase  of  the  capacity  of  the  bulb  we  must 
subtract  the  amount  the  water  is  compressed  for  each  meter's 
pressure,  that  is,  about  0.000064,  according  to  MM.  Colladon 
and  Sturm  ;  this  yields  0.000044  for  the  expansion  of  the  bulb 
for  an  increase  of  pressure  of  1  m.  of  mercury. 

Thus  to  make  the  correction  in  our  determinations,  it  will 
suffice  to  add  to  the  coefficient  6  T  of  the  expansion  of  the 
bulb  by  heat,  the  expansion  produced  by  the  rise  of  pressure, 

which  is  0.000044  g/ 


In  the  above  experiments  the  change  in  the  capacity  of  the 
bulb  through  an  increase  of  pressure  was  determined  at  ordinary 
temperature;  yet  it  is  really  its  value  at  the  temperature  of 
100°  that  we  need  to  know  in  order  to  allow  for  it  in  our 
determinations  of  the  rate  of  expansion  of  gases,  and  it 
might  be  objected  that  at  100°  this  change  would  not  be  the 
same.  Yet  it  will  be  noted  that  this  introduces  a  very  minute 
correction  which  may  be  neglected  since,  at  most,  it  changes 
the  fourth  decimal  of  the  coefficient  of  expansion,,  Thus  it 
may  be  assumed  without  inaccuracy  that  the  compressibility  of 
glass  is  the  same  at  100°  as  at  the  ordinary  temperature, 

The  formula  in  accordance  with  which  the  determinations 
have  been  calculated  is  the  following: 


(ir  +  &')    i+dr  +0.000044    —  '  h  ~H  -) 


The  following  table  contains  the  results  obtained  with  these 
two  forms  of  apparatus. 


133 


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MEMOIRS     OK 

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oo  o  o  o  o  oo 

CO  ~*  TH  GO  Oi  ""*  <N  CD 

CO  CO  t-  T*  CO  CO  CO  CN 

§O5  ^^  ^  O  TH  ^H  Oi 

GO  T-^  CO  CO  CN  CO  O 

i-lr-l  r-li-lTHiH  <M(M 


SSBS 

O    O    O   O 


o  »o  »o 


^   ^   Tii   ^41 


1 


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O^  CD«O^t-^  ^^T 

»CCD  »OiOiO»O  t~   t» 


-H     -*     Oi     CO  T-H     t- 

CD    00    O    TH  G^    T-H 

CD  eg  t^  t^         oj  qi 


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O    O  O    O    O    O 


y   co  t^  co  co 

Ci    Oi    Oi    OS 
QQ 


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O    O 


S?SJ 

CO    lO    O    3 


CO    T}<    CO    »O 
00    CO    OO    00 

8888 

o  c>  o  o 


OO    00    1O    CD  P    CO 

lO    »O    »O    O  iO    -^JH 

CO    CO    CO    CO  00    00 


CO    OO    CD    <N 

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: 

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CO    ^  ^ 


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t-  t-  t-  t- 

134 


(>l    C^    O1    CO 

o:  os  os  os 


t—  t-  t—  t- 


EXPANSION    OF    GASES 

This  Table  shows  that  the  coefficient  of  expansion  of  dry 
air  increases  in  a  marked  way  with  the  pressure,  and  conse- 
quently confirms  the  result  already  reached  by  the  determina- 
tions, page  56  [page  126],  made  under  pressures  lower  than 
that  of  the  atmosphere. 

Summing  up,  we  have  found  the  following  figures  for  the 
value  of  the  coefficient  of  expansion  of  air  under  various  pres- 
sures : 


Pressure  at  0°. 

Pressure  at  100° 

Density  of  air  at 
0°,  that  of  air  at  0° 
under  a  pressure  of 
760  mm.  being 
taken  as  unity. 

1  +  100  a 

109.72 

149.31 

0.1444 

1.36482 

174.36 

237.17 

0.2294 

1.36513 

266.06 

395.07 

0.3501 

1.36542 

374.67 

510.35 

0.4930 

1.36587 

375.23 
760.00 

510.97 

0.4937 
1.0000 

1.36572 
1.36650 

1678.40 

2286.09 

2.2084 

1.36760 

1692.53 

2306.23 

2.2270 

1.36800 

2144.18 

2924.04 

2.8213 

1.36894 

3655.56 

4992.09 

4.8100 

1.37091 

The  third  column  of  the  table  comprises  the  densities  of  the 
gas  at  the  temperature  of  melting  ice  ;  it  will  be  seen  that 
these  vary  from  0.1444  up  to  4.8100,  that  is,  from  1  to  33.3, 
and  for  so  great  a  change  in  density,  the  coefficient  of  expan- 
sion of  the  gas  changes  only  from  0.3648  to  0.3709. 

The  above  determinations  therefore  prove  that  the  law 
assumed  correct  by  physicists,  viz.,  that  air  expands  [on  heat- 
ing] the  same  fraction  of  its  volume  at  0°,  whatever  its  density, 
is  not  accurate  ;  air  expands,  between  the  same  temperature- 
limits,  by  amounts  which  are  greater  in  proportion  as  the 
density  of  the  gas  is  higher,  or,  in  other  words,  as  the  mole- 
cules are  closer  together. 

Similar  determinations  were  made  with  carbonic  acid  gas  by 
means  of  the  two  pieces  of  apparatus  described  :  they  gave  the 
following  results  : 

135 


MEMOIRS    ON 


Apparatus  I. 


Apparatus  II. 


JET  

..759.94mm. 

760.03  mm. 

t  

.     145° 

13.9° 

h  

...982.75  mm 

982.74  mm. 

V 

0.00361 

0.00362 

V 

H+h... 

.1742.69mm. 

1742.77  mm. 

H'  

..759.86 

759.83 

T'  

..100.0° 

99.99° 

£'  

.  .  .  15  8 

15.6 

h'  

.1627.81  mm. 

1627.95  mm. 

H'+h'  . 

.2387.67 

2387.78 

v<   

....0.00366 

0.00367 

V 

1+lOOa. 

...1.37520 

1.37525 

757.69  mm.     757.79  mm. 

11.3°  11.2° 

2831.37mm.  2831.19  mm. 
0.00190  0.00190 

3589.06  mm.  3588.98  mm. 

758.11  758.41 

99.93°  99.94° 

11.3  11.4 

4200.50  mm.  4201.05  mm. 

4958.61  4959.46 

0.00190  0.00190 


1.38586 


1.38609 


Combining  these  results  with  those  given  in  the  earlier 
memoir,  volume  IV,  pages  57  and  60  [  pages  109  and  113],  we 
have  for  carbonic  acid  gas  : 


Pressure  at  0°. 

Pressure  at  100°. 

Density  of  the 
gas  at  0°. 

1  +  lOOa 

758.47  m  m. 

1034.54  m  m. 

1.0000 

1.36856 

901.09 

1230.37 

1.1879 

1.36943 

1742.73 

2387.72 

2.2976 

1.37523 

3589.07 

4759.03 

4.7318 

1.38598 

It  is  evident  that  the  rate  of  expansion  of  carbonic  acid  gas 
increases  more  rapidly  with  the  pressure  than  does  that  of 
atmospheric  air. 

SECOND  PART. 

Experiments  to  determine  the  Rate  of  Expansion  of 
Gases  under  Constant  Pressure. 

In  all  the  experiments  described  up  to  the  present  the  rate 
of  expansion  of  the  gas  has  been  determined  indirectly.  We 
measure  directly  the  increase  in  the  tension  which  the  gas, 
maintained  at  a  constant  volume,  exerts  by  reason  of  the  rise 
in  temperature,  and  from  this  we  calculate  the  rate  of  expan- 
sion on  the  basis  of  Mariotte's.  Law.  Yet  it  may  be  objected 
that  it  has  not  been  shown  that  this  law  is  absolutely  exact 
even  for  air,  and,  consequently,  that  the  increments  deter- 
mined in  the  rates  of  expansion  under  different  pressures  may 

136 


EXPANSION    OF    GASES 

only  point  to  the  fact  that  Mariotte's  Law  is  not  rigorously 
true. 

This  objection  does  not  seem  to  me  to  be  justified,  for  sev- 
eral reasons.  As  a  matter  of  fact  Dulong  and  Arago  did  not  in 
their  brilliant  research  discover  any  constant  variation  even  at 
pressures  as  high  as  27  atmospheres,  which  in  any  case  shows 
that,  between  the  limits  of  pressure  of  1  and  27  atmospheres, 
Mariotte's  Law  is  practically  exact  ;  hence  we  may  conclude 
that  it  would  be  rigorously  accurate  for  differences  of  pressure 
as  small  as  those  observed  in  our  researches  on  any  given  gas, 
at  0°  and  at  100°.  It  is  clear  that,  were  there  a  variation 
which  such  small  differences  of  pressure  could  render  evident 
in  measurements  of  the  rate  of  expansion,  this  variation  would 
certainly  be  revealed  in  a  very  marked  degree  by  the  great  dif- 
ferences of  pressure  in  determinations  made  with  as  much  care 
as  those  of  the  distinguished  physicists  I  have  named. 

I  should  state,  too,  that  my  experiments  were  carried  out 
under  precisely  those  conditions  which  would  be  most  favor- 
able for  exactness  in  Mariotte's  Law,  since  it  is  the  gas  heated 
to  the  temperature  of  100° — consequently,  at  the  very  time 
when  it  is  farthest  removed  from  its  condensation  point — that 
it  is  subjected  to  the  greatest  pressure. 

Finally,  it  should  be  noted  that,  in  the  parallel  determina- 
tions made  upon  the  compressibility  of  different  gases  under 
one  and  the  same  pressure,  it  was  shown  that  the  gases  which 
do  not  follow  Mariotte's  Law  show  a  greater  diminution  of 
volume  than  should  take  place  according  to  the  Law.  There- 
fore in  my  experiments,  neglecting  the  changes  occurring  in  the 
molecular  forces  on  account  of  the  difference  in  temperature, 
the  volume  of  the  gas  at  100°  ought  to  be  smaller  than  what 
exactly  accords  with  Mariotte's  Law  ;  so  that  the  variation  in 
Mariotte's  Law  would  tend  to  diminish  the  coefficient  of  expan- 
sion with  [increase  of]  the  pressure,  instead  of  increasing  it  as 
we  have  found  in  our  experiments. 

After  all,  to  avoid  leaving  any  doubt  upon  this  important 
point  in  the  dynamical  theory  of  gases,  I  made  a  new  series  of 
determinations  by  a  method  in  which  the  increase  in  the  vol- 
ume of  the  gas  is  measured  directly,  while  it  remains  under 
practically  the  same  pressure  at  0°  and  at  100°.  This  method 
J  137 


MEMOIRS    ON 

is  clearly  the  only  one  that  can  be  used  with  gases  which  do 
not  follow  Mariotte's  Law  for  slight  changes  of  pressure. 

I  shall  describe  briefly  the  apparatus  I  have  used  in  these 
determinations  and  which  is  based  upon  the  same  principle  as 
that  used  by  M.  Pouillet  in  his  air  pyrometer.  It  is  shown  in 
Fig.  3. 

Z 


FIG.  3. 

A  glass  bulb  sealed  to  a  capillary  tube  is  placed  in  a  tin-plate 
vessel  MN  (Fig.  13,  Volume  IV)  [page  96].  The  tube  is 
cemented  into  the  little  three-way  tube  mno.  In  the  side- 
tubulure  o  is  cemented  a  short  straight  piece  of  capillary  tub- 
ing, or  else  a  tube  of  the  shape  of  abed,  Fig.  1,  Volume  V  [page 
128],  and  containing  some  pellets  of  gum  mastic, — according  as 
we  must  work  under  pressures  lower  or  higher  than  that  of  the 
atmosphere.  Into  the  third  tubulure  n  is  cemented  the  bent 
capillary  tube  EF  connecting  with  the  tube  FH  in  which  the 
increase  of  volume  of  the  air  is  measured.  The  latter  is  so 
chosen  that  the  quantity  of  air  which  fills  it  to  a  when  the  bulb 

138 


EXPANSION    OF    GASES 

is  in  melting  ice,  occupies,  when  the  bulb  is  in  [the  vapor  of] 
boiling  water,  most  of  the  space  down  to  a  mark  p  made  upon 
the  narrower  tube  below.  The  tube  FH  is  cemented  with 
mastic  into  the  tubulure  A  of  an  iron  support  provided  with 
taps.  Into  the  second  tubulure  B  is  cemented  a  glass  tube  BI, 
a  meter  long  in  experiments  made  under  atmospheric  pressure. 
This  tube  was  replaced  by  one  of  3  meters'  length  when  work- 
ing with  greater  pressures. 

The  iron  support  has  two  taps  R  and  R'.  The  first  tap  R  is 
traversed  by  a  single  hole  and  serves  to  draw  off  a  part  of  the 
mercury  contained  in  the  apparatus.  The  second  tap  R 
is  bored  with  two  holes  at  right  angles  to  each  other,  and 
serves  to  connect  the  tube  FH,  according  to  the  position  given 
it,  with  the  barometric  tube  BI,  or  directly  with  the  outside. 
This  arrangement  is  clearly  seen  in  Fig,  4  [page  138],  which 
represents  a  vertical  section  of  the  support  and  the  two  posi- 
tions (a)  and  (&)  of  the  tap  R.  This  support  is  fastened  to  a 
cast  tripod  provided  with  levelling  screws,  upon  which  is  fitted 
a  glass  jacket  filled  with  water  for  keeping  the  expansion  reser- 
voir at  a  known  temperature.  This  jacket  consists  of  a  rect- 
angular box  two  of  whose  opposite  sides  are  made  of  glass. 

The  experiment  is  then  made  as  follows  : 

The  bulb  being  surrounded  with  melting  ice,  the  tube  op  open 
and  connected  with  the  apparatus  which  was  used  before  to  dry 
the  air,  mercury  is  poured  into  the  tube  BI  until  it  reaches  the 
level  of  a.  The  tap  R  being  in  position  (a),  the  mercury  of 
course  rises  to  the  same  level  in  the  two  communicating  tubes. 
The  tube  op  is  closed  by  means  of  a  lamp,  [the  height  of]  the 
barometer  is  recorded,  as  is  also  the  temperature  of  the  water 
in  the  jacket,  which  has  been  carefully  stirred  from  time  to 
time  by  means  of  the  stirrer  ffgg'  which  is  moved  up  and  down 
in  a  vertical  plane  so  as  to  make  it  pass  through  all  strata  of 
the  liquid. 

After  removing  the  ice,  the  water  in  the  vessel  M  is  brought 
to  boiling.  To  keep  the  two  columns  of  mercury  at  about  the 
same  point,  it  becomes  necessary  to  draw  off  mercury  by  open- 
ing the  tap  R.  A  part  of  the  air  in  the  bulb  thus  passes  into 
the  tube  FH;  the  two  columns  are  brought  approximately  to 
the  same  level  0,  and  the  difference  of  height  is  determined 

139 


MEMOIES    ON 

accurately  by  means  of  the  cathetometer; l  at  the  same  time  the 
[height  of  the]  barometer  and  the  temperature  of  the  jacket 
are  recorded.  The  water  filling  the  jacket  was  continuously 
stirred  for  at  least  a  quarter  of  an  hour  before  beginning  the 
observations,  to  give  it  a  uniform  temperature  which  would  at 
the  same  time  be  that  of  the  air  enclosed  in  the  tube  FH. 

To  be  able  from  this  experiment  to  calculate  the  coefficient 
of  expansion  of  air,  we  must  know  the  capacity  of  the  bulb,  the 
volume  v  from  E  to  a  of  the  air  in  the  tube  FH  when  the  bulb 
is  in  melting  ice,  and  the  volume  v'  from  E  to  p  which  is  filled 
by  air  when  the  bulb  is  in  [the  vapor  of]  boiling  water.  The 
first  is  easily  found  by  filling  the  bulb  with  mercury  at  0°, 
after  having  made  it  boil  for  a  while  in  the  apparatus.  (See 
volume  IV,  page  22  [page  82].) 

The  two  volumes  v  and  v'  are  determined  in  the  following 
way: 

The  drawn-out  end  of  the  tube  op  is  broken  off  to  allow  com- 
munication between  the  interior  and  the  outside  air,2  and  mer- 
cury is  poured  into  the  tube  BI  until  this  liquid  entirely  fills 
the  tube  FH  as  far  as  y  on  the  capillary  tube.  The  tap  R'  is 
turned  into  the  position  (#).  There  is  then  no  connection 
between  the  tubes  FH  and  BI,  but  the  mercury  from  FH  flows 
out  by  the  opening  0'.  This  mercury  is  caught  in  a  flask. 
Mercury  is  allowed  to  run  out  until  the  meniscus  comes  exactly 

1  There  was  danger  lest  the  jacket  full  of  water  would  give  rise,  on 
account  of  refraction,  to  deviations  of  the  rays  which  come  from  the 
menisci :  a  very  simple  test  showed  me  there  was  no  appreciable  devia- 
tion, at  any  rate  in  the  places  where  the  readings  were  made.  The  tube 
op  being  open,  the  mercury  meniscus  was  adjusted  at  points  all  along 
the  tube  FH  in  succession.  It  was  seen,  with  the  aid  of  the  glass  of  the 
cathetometer,  that  in  all  these  positions  the  menisci  were  at  the  same 
level  in  the  two  tubes  FH  and  BI. 

a  To  prevent  the  entrance  of  moist  air  into  the  apparatus,  care  is 
taken  first  to  connect  the  tube  op  with  the  drying  apparatus  by  means 
of  a  rubber  tube.  In  many  experiments,  chiefly  those  made  upon  gases 
other  than  atmospheric  air,  the  point  of  the  tube  op  is  not  broken  off. 
The  bulb  being  in  the  [vapor  of  1  boiling  water,  mercury  is  poured  into 
the  tube  BI  so  that  the  liquid  rises  into  the  capillary  part  EF  of  the 
tube  FH',  the  volumes  v  and  v'  are  then  calibrated  as  usual. 

140 


EXPANSION     OF    GASES 

to  the  position  at  a  that  it  had  in  the  first  part  of  the  experi- 
ment: this  is  done  with  great  precision  with  the  aid  of  the  glass 
of  the  cathetometer.1  The  mercury  which  has  flowed  out  is 
weighed,  and  from  this  the  volume  v  is  calculated. 

The  mercury  is  then  run  out  until  the  meniscus  coincides 
with  p.  The  weight  of  mercury  drawn  off,  added  to  that  which 
gave  the  volume  v,  will  give  us  the  volume  v'.  It  is  clear  there 
is  a  correction  to  be  made  on  account  of  the  temperature;  if  p 
and  p'  represent  the  weights  of  mercury  drawn  off  and  t  the 
temperature  of  the  water  of  the  jacket  at  the  time  of  the  cali- 
bration, the  weights  of  mercury  at  0°  which  will  occupy  the 
volumes  v  and  v',  and  which,  consequently,  actually  represent 

these  volumes,  are  p  (1  +  i-)  and^r  (1  +  ~)> 


It  is  necessary  to  add  to  these  volumes  v  and  v'  the  small 
volume  of  the  capillary  tubing  outside  the  vessel  in  which  the 
water  is  boiling.  This  volume  was  determined  by  a  preliminary 
calibration.  On  the  other  hand,  since  the  temperature  of  the 
air  contained  in  these  tubes  is  somewhat  uncertain,  it  is  desir- 
able that  this  volume  should  be  extremely  small.  In  my  appa- 
ratus it  never  exceeded  ^^^  of  the  capacity  of  the  bulb. 

In  order  to  adapt  the  same  apparatus  for  measuring  the  rate 
of  expansion  of  air  under  high  pressures,  the  lateral  tube  op  is 
replaced  by  the  twice-bent  tube  abed  of  Fig.  1  [page  128],  and 
dry  air  is  forced  into  the  bulb,  while  mercury  is  poured  into  the 
tube  BI.  When  the  desired  pressure  has  been  got  in  the  bulb, 
the  gum  mastic  in  the  tube  abed  is  melted  so  as  to  close  the 
apparatus  hermetically  ;  the  bulb  is  surrounded  with  melting 
ice  and  the  meniscus  is  adjusted  to  the  mark  a  with  the  aid  of 
a  cathetometer.  The  meniscus  in  the  tube  BI  is  brought  in 
line  with  a  second  cathetometer.  In  these  measurements  the 
precautions  noted  on  page  59  [page  129]  are  followed  closely. 

After  removing  the  ice,  the  water  in  the  vessel  is  raised  to 
boiling,  and  mercury  is  drawn  off  so  as  to  make  the  level  coin- 
cide with  0. 

The  height  of  the  raised  column  of  mercury  is  measured  ;  it 

1  The  flow  of  the  mercury  is  made  as  slow  as  may  be  desired  by  turn- 
ing the  tap  to  the  proper  extent:  it  is  easy  to  adjust  the  meniscus  in 
this  way  within  about  -fa  of  a  millimeter. 

141 


MEM OIKS    ON 

is  practically  the  same  as  that  of  the  first  part  of  the  determi- 
nation. 

If  Hand  H'  represent  the  barometric  heights  at  the  time  of 
the  readings  for  [the  temperatures  of]  melting  ice  and  boiling 
water,  and  h  and  h'  the  differences  of  level  of  the  menisci  in 
the  tubes  of  the  apparatus,  we  evidently  have  the  equation 


hence 

(H'  +  h')  (1  +  6  T) 


V    1  +  at 

The  quantity  a  enters  into  the  denominator  of  the  second 
member  ;  but  as  it  affects  the  result  only  slightly,  we  make  use 
of  the  method  of  successive  approximations,  that  is,  an 
approximate  value  is  given  «,  from  this  the  value  of  a  in  the 
first  member  is  calculated  and  this  is  then  substituted  in 
the  second  member  and  yields  t'he  final  value  of  1  +  a T. 

In  this  method  the  greatest  care  must  be  exercised  in  the 
determination  of  the  volumes  F,  v  and  v',  and,  even  more,  in 
the  determination  of  the  temperature  t'.  There  is,  finally, 
another  very  important  matter — the  perfect  drying  of  the  tube 
FH.  This  tube  has  a  large  capacity  and,  on  account  of  the 
arrangement  of  the  apparatus,  cannot  be  heated  while  it  is 
exhausted.  In  my  experiments  this  tube  was  thoroughly  dried 
at  a  high  temperature  before  being  cemented  into  its  tubulure, 
and,  when  the  apparatus  was  completely  set  up,  a  little  mercury 
was  poured  into  the  communicating  tubes;  the  tap  R  was 
turned  to  a  position  intermediate  between  (a)  and  (#),  and  the 
apparatus  exhausted,  the  bulb  being  surrounded  by  the  vapor 
of  boiling  water.  By  exhausting  a  great  many  times  and  then 
allowing  dry  air  to  enter  slowly,  the  moisture  should  not  only 
be  completely  removed  from  the  bulb  but  also  from  the  tube  in 
which  the  expansion  is  measured. 

The  table  below  contains  the  results  obtained  in  the  experi- 
ments made  by  this  method,  at  atmospheric  pressure,  upon  air, 
hydrogen,  carbonic  acid  gas,  protoxide  of  nitrogen,  oxide  of 
carbon,  sulphurous  acid  gas,  and  cyanogen. 

The  second  part  of  the  table  contains  [the  results  of]  experi- 

142 


EXPANSION    OF     GASES 

meuts  made  upon  atmospheric  air,  hydrogen,  and  carbonic  acid 
gas  under  higher  pressures. 


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143 


MEMOIRS    ON 

Atmospheric  air  gives  figures  a  little  higher  than  the  mean 
of  earlier  determinations;  yet  the  difference  is  inappreciable;  it 
may  be  attributed  also  to  the  fact  that  air  does  not  conform 
rigorously  to  Mariotte's  Law. 

My  earlier  determinations  gave  for  hydrogen  the  same 
coefficient  of  expansion  as  for  air.  The  new  experiments 
assign  to  hydrogen  a  coefficient  slightly  lower  than  that  of  air. 
Hr.  Magnus  has  already  reached  a  similar  result  (Annales  de 
Chimie  et  de  Physique,  volume  IV,  page  334),  but  the  differ- 
ences are  so  small  that  it  is  difficult  to  decide  the  question;  they 
are  within  the  limits  of  the  errors  of  observation.  As  a  matter 
of  fact,  there  are  in  Magnus'  determinations  with  air  many 
figures  which  are  still  lower  than  those  he  has  found  for  hydro- 
gen; so  that  the  question  does  not  seem  to  me  settled.  It  will 
be  seen  later  that  the  experiments  made  upon  the  rate  of 
expansion  under  higher  pressures  decide  the  matter  in  a  very 
clear  way. 

The  hydrogen  was  prepared  from  very  pure  zinc;  it  was 
passed  through  a  wash  bottle  containing  water,  two  tubes  a 
meter  long  full  of  pumice-stone  soaked  with  a  concentrated 
solution  of  potash,  a  tube  of  equal  length  full  of  pumice  stone 
soaked  with  a  solution  of  silver  sulphate.  Beyond  the  air 
pump  it  traversed  two  tubes  a  meter  long  full  of  pumice  stone 
soaked  with  concentrated  sulphuric  acid,  and  a  tube  filled  with 
small  bits  of  caustic  potash.  The  latter  was  to  hold  back  the 
small  quantity  of  sulphurous  acid  gas  which  might  be  formed 
through  the  interaction  of  the  hydrogen  gas  and  the  sulphuric 
acid.  This  precaution  had  been  neglected  in  the  determina- 
tions of  the  first  memoir,  yet  I  have  never  perceived  any  odor 
from  the  presence  of  sulphurous  acid  in  any  of  these  experi- 
ments. 

Oxide  of  carbon  gave  the  same  figure  as  in  the  earlier 
researches  (volume  IV,  page  52  [page  109]  ). 

The  coefficients  of  expansion  of  carbonic  acid  gas  and  pro- 
toxide of  nitrogen  determined  by  this  method  are  higher  than 
those  obtained  by  the  earlier  methods  (volume  IV,  pages  52,  56 
and  57  [pages  109,  113,  115]  );  this  is  unquestionably  due  to  the 
fact  that  these  gases  do  not  exactly  conform  to  Mariotte's  Law, 
and  that  their  volumes  at  100°,  under  a  pressure  higher  than 

144 


EXPANSION    OF    GASES 

that  to  which  they  are  subjected  at  this  temperature  in  the 
earlier  methods,  are  smaller  than  they  ought  to  be  according 
to  this  Law.  We  must  expect  to  find  similar  results  with  all 
gases  more  compressible  than  air. 

The  coefficients  of  expansion  of  sulphurous  acid  [gas]  and 
cyanogen  are  much  higher  than  those  of  other  gases.  My 
earlier  researches  (volume  IV,  pages  52  and  57  [pages  109  and 
114]  )  had,  on  the  other  hand,  assigned  them  figures  very  little 
higher  than  the  coefficient  of  expansion  of  atmospheric  air. 
The  variations  may  be  attributed  to  the  fact  that,  sulphurous 
[acid]  gas  and  cyanogen  being  much  more  compressible  than 
air,  their  volume  at  100°,  calculated  from  the  change  of  ten- 
sion, is  much  too  low  and,  consequently,  gives  too  small  a 
coefficient  of  expansion.  In  an  endeavor  to  verify  this  sup- 
position by  means  of  direct  experiments,  and  after  many  trials, 
I  found  that  there  had  been  a  serious  error  in  my  former 
determinations  of  sulphurous  acid  [gas]  and  cyanogen. 

I  have  always  had  to  face  the  difficulty  of  drying  sulphurous 
acid  gas  completely,  the  presence  of  a  trace  of  moisture  being 
able,  in  the  case  of  this  very  soluble  gas,  to  cause  much  greater 
variations  than  in  other  gases.  My  earliest  experiments  had 
given  for  sulphurous  acid  [gas]  figures  much  higher  than  those 
to  which  I  was  led  in  my  former  research;  but  I  discovered  that 
these  figures  became  lower  in  proportion  as  the  gas  was  more 
slowly  admitted  into  the  bulb, — which  I  most  naturally  attrib- 
uted to  more  perfect  drying, — and  it  was  only  by  having  the 
gas  enter  extremely  slowly,  compelling  it  to  remain  for  a  long 
time  in  the  tubes  full  of  pumice  stone  soaked  with  concen- 
trated sulphuric  acid  before  introducing  it  into  the  bulb,  that 
I  succeeded  in  securing  constant  figures.  Working  in  this 
way,  a  source  of  error  is  introduced  which  then  escaped  me; 
some  dry  air  evidently  entered  the  bulb  along  with  the  sulphur- 
ous acid  gas.  The  proportion  of  this  air  was  greater,  the 
slower  the  introduction  of  the  sulphurous  acid  gas.  Now  the 
presence  of  a  small  amount  of  air  is  sufficient  to  lower  appreci- 
ably the  coefficient  of  expansion  of  sulphurous  acid  [gas],  since 
the  latter  gas  expands  under  these  circumstances  as  if  it  were 
under  a  very  low  pressure,  and  the  coefficient  of  expansion  of 
sulphurous  acid  [gas]  falls  very  rapidly  with  the  pressure, 

145 


MEMOIKS    ON 

I  thought  at  that  time  that  the  entrance  of  air  must  be  due 
to  the  fact  that  the  apparatus  (perhaps  the  taps  of  the  pump 
through  the  action  of  the  acid  gas)  had  not  remained  gas-tight 
during  the  long  time  the  gas  was  making  its  way  in.  I  am  not 
prepared  to  assert  this  was  not  the  case,  yet  1  can  say  that  the 
apparatus  was  always  tested  with  great  care  each  time  before 
commencing  a  series  of  experiments  with  any  particular 
gas. 

Yet  there  is  another  source  of  error  against  which  I  was  not 
sufficiently  on  my  guard  in  my  earlier  experiments.  It  lay  in 
the  great  difficulty  met  with  in  freeing  the  pumice  stone  and 
sulphuric  acid  from  air  mechanically  held  or  absorbed;  thus,  I 
found,  in  the  experiments  with  sulphurous  acid  [gas],  that 
after  the  apparatus  had  been  exhausted  three  or  four  times  in 
succession,  at  least  to  1  or  2  centimeters,  and  sulphurous  acid 
gas  had  been  introduced  each  time,  the  gas  in  the  bulb  still 
showed  on  testing  an  appreciable  amount  of  air  mixed  in.  In 
the  ordinary  determinations  with  gases  other  than  atmospheric 
air,  I  was  accustomed  to  exhaust  at  least  ten  or  twelve  times; 
in  the  experiments  with  sulphurous  acid  gas  I  contented  myself 
with  only  three  or  four  times,  because  of  the  very  long  time 
required  for  each  filling.  In  the  experiments  with  cyanogen, 
only  two  exhaustions  were  made,  on  account  of  the  difficulty  of 
preparing  a  considerable  quantity  of  this  gas  in  a  pure  state. 

Sulphurous  acid  gas  in  the  recent  determinations  was  pre- 
pared by  the  action  of  mercury  upon  sulphuric  acid;  the  gas 
passed  through  a  long  inclined  U-tube  full  of  concentrated  sul- 
phuric acid  which  the  bubbles  traversed  very  slowly;  from  this 
it  made  its  way  to  the  bulb  through  a  tube  connecting  with  the 
small  air  pump.  This  arrangement  permitted  the  exhaustion, 
not  only  of  the  receiving  bulb,  but  also  of  the  generating  appa- 
ratus. Besides,  it  was  easy  to  prove,  by  means  of  the  com- 
municating tubes  .PIT  and  BI,  that  the  apparatus  was  perfectly 
gas  tight. 

The  bulb  had  in  this  way  been  filled  with  perfectly  pure  sul- 
phurous acid  gas.  I  satisfied  myself  after  the  determinations 
were  over,  by  breaking  off  the  tip  of  the  tube  op  under  mer- 
cury and  driving  out  part  of  the  gas  by  pouring  mercury  into 

146 


EXPANSION     OF     GASES 

the  tube  BI.  The  gas  was  completely  absorbed  by  a  solution  of 
potash.i 

A  similar  arrangement  was  used  in  the  work  on  cyanogen. 
This  gas  was  prepared  by  decomposing  cyanide  of  mercury  with 
the  aid  of  heat;  it  passed  through  a  long  column  of  concen- 
trated sulphuric  acid. 

If  we  adopt  the  figures  found  for  the  coefficients  of  expansion 
of  the  various  gases  by  this  last  method,  which  is  the  only  one 
capable  of  giving  comparable  results  when  we  wish  to  know  the 
rates  of  expansion  of  gases  which  do  not  follow  Mariotte's  Law, 
it  is  apparent  that  the  various  gases  show  very  different  co- 
efficients of  expansion.  We  have  found,  as  a  matter  of  fact,  for 
these  coefficients: 

Hydrogen 0.36613 

Atmospheric  Air 0.36706 

Oxide  of  Carbon 0.36688 

Carbonic  Acid  Gas 0.37099 

Protoxide  of  Nitrogen 0.37195 

Cyanogen 0.38767 

Sulphurous  Acid  Gas 0.39028 

I  have  already  shown  above  that  the  coefficients  of  expansion 
of  carbonic  acid  gas  and  protoxide  of  nitrogen  were  higher 
when  determined  by  the  last  method  than  when  calculated  from 
the  changes  in  tension.  The  variations  are  much  greater  for 
the  very  compressible  gases,  such  as  cyanogen  and  sulphurous 
acid  gas,  as  may  be  understood  from  the  following  results, 
which  have  been  reached  in  the  same  series  of  determinations 
as  the  figures  given  in  the  table  above.  As  a  matter  of  fact,  in 
order  to  obtain,  with  the  apparatus  of  Fig.  3  [page  138],  the 
variations  of  tension  in  the  gas  occupying  a  constant  volume, 
when  it  is  carried  from  the  temperature  of  melting  ice  to  that 
of  boiling  water,  it  is  only  necessary  to  keep  the  level  of  the 
mercury  at  a  in  the  tube  FH  while  the  bulb  is  in  [the  vapor  of] 
boiling  water,  and  to  measure  the  difference  of  level  between  a 

1  It  remains  to  be  decided  whether  sulphurous  acid  gas  is  completely 
dried  by  concentrated  sulphuric  acid,  and  whether  it  did  not  carry  with 
it  a  minute  quantity  of  the  latter  acid.  This  point  seemed  to  be  hard 
to  decide  by  direct  experiment;  the  coefficient  of  expansion  of  the  gas 
is  perhaps  appreciably  changed  by  the  presence  of  an  infinitesimal 
quantity  of  [water]  vapor. 

147 


MEMOIRS    ON 


and  the  meniscus  of  the  mercury  pushed  up  in  the  tube  BL 
These  determinations  were  made,  in  fact,  in  the  three  experi- 
ments upon  gaseous  sulphurous  acid  and  in  the  two  experiments 
upon  cyanogen.  With  the  values  for  H,  t,  h,  v,  and  H+h  of 
the  table  above  [page  143]  it  is  only  necessary  to  combine  the 
following: 


Sulphurous  Acid  Gas 


Cyanogen 


II 


III 


H' 

759  31  mm 

760.71  mm. 

762.13  mm. 

T1 

99.98  ° 

100.03° 

lOO.OSo 

f 

19.29° 

19.88  ° 

18.42o 

h' 

..288.62mm. 

286.19mm. 

284.30  mm. 

H'  +  ft'.  1047.93  mm.   1046.90  mm.  1046.43  mm. 

v'  21.44  gr.          25.79  gr.         28.20  gr. 

1  +  100  a..  1.38439  1.38451  1.38470 

Thus,  we  have  found: 


I  II 

763.07  mm.  764.07  mm. 

100.12°  100.15° 

20.94°  19.16° 

289.23  mm.  287.62  mm. 

1052.30mm.  1051.69  mm. 

22.80  gr.  25.62gr. 

1.38282  1.38298 


For  Sulphurous  Acid  Gas: 
By  direct  measurement  of  expansion. 


0.39094 

0.38987 
0.39004 


By  calculation,  from  the  change 
of  tension. 
0.38439 
0.38451 
0.38470 


Mean 0.39028 

0.38766 
0.38768 


For  Cyanogen: 


0.38453 : 

0.38282 
0.38298 


0.38290 


Mean 0.38767 

I  have  stated  above  that  the  coefficient  of  expansion  of  sul- 
phurous acid  gas  rises  quite  rapidly  with  the  pressure;  this  may 
be  observed  in  the  following  experiment,  begun  by  filling  the 
bulb,  while  cooled  with  ice,  and  the  expansion-tube  FIf  down  to 
/?,  with  sulphurous  acid  gas.  The  tube  op  was  then  sealed 
with  the  lamp  and,  by  pouring  mercury  into  the  tube  BI,  the 
gas  contained  in  the  tube  FH  was  forced  back  into  the  bulb. 

1  This  figure  differs  little  from  the  mean  assumed  by  Hr.  Magnus,  but 
from  three  determinations  which  gave  too  divergent  figures,  viz., 
0.3897;  0.3839;  0.3832. 

148 


EXPANSION     OF    GASES 

In  other  respects  the  determination  is  carried  out  as  has 
been  described  in  volume  IV,  page  43  [page  99]  ;  we  have : 

H  =  761.33  mm.  H'  =  761.08  mm. 

£  =  18.83  °  T  =  100.04° 

h  =  221 .40  mm.  t'  =  19.10  ° 

v  =  25.36  gr.  h'=  226.56  mm. 

H-\-  h  =  982.73  mm.  H'  +  h'  =  987.64  mm. 

v'  =  1780.44  gr. 
1+  ;  00  a=  1.39804. 

Thus,  for  a  change  in  pressure  as  slight  as  that  from  760  mm. 
to  980  mm.,  the  coefficient  of  expansion  of  sulphurous  acid 
[gas]  has  changed  from  0.3902  to  0.3980,  and  the  gas  under 
the  pressure  of  980  mm.  is  not  even  at  0°  near  its  point  of  con- 
densation. 

It  is  likely,  judging  from  this,  that  vapors  have  coefficients 
of  expansion  very  different  from  that  of  air  at  points  slightly 
removed  from  their  points  of  condensation — consequently, 
under  the  conditions  where  we  usually  meet  them  in  our  exper- 
iments for  determining  their  densities. 

Let  us  now  turn  to  the  second  part  of  the  table  [page  143] 
which  contains  determinations  made  under  a  pressure  of 
2530  mm.  (about  3.33  atmos.)  with  three  gases,  atmospheric  air, 
hydrogen,  and  carbonic  acid  gas.  The  very  striking  fact  is 
there  apparent  that  hydrogen  has  maintained  practically  the 
same  coefficient  of  expansion  as  under  atmospheric  pressure ; 
whereas  air,  and,  above  all,  carbonic  acid  gas  show  a  very 
marked  increase  in  their  coefficients. 

The  variation  in  rates  of  expansion  of  atmospheric  air  and 
carbonic  acid  gas  is  far  more  noteworthy  in  those  experiments 
where  the  pressure  is  the  same  at  0°  and  at  100°,  than  in  those 
where  the  rates  of  expansion  were  calculated  from  the  change 
of  tension. 

At  the  same  time  it  is  clear  that  in  proportion  as  the  pres- 
sure under  which  the  gases  are  studied  is  greater,  so  much  the 
more  marked  become  the  variations  among  their  coefficients  of 
expansion.  Hydrogen  and  atmospheric  air,  which  have  prac- 
tically the  same  rate  of  expansion  under  ordinary  barometric 
pressure,  show  very  marked  differences  when  they  are  subjected 
to  pressures  three  or  four  times  as  great. 

149 


MEM  OIKS    ON    EXPANSION    OF    GASES 

Conclusions. 

To  sum  up,  my  determinations  do  not  confirm  the  two  fun- 
damental laws  of  the  theory  of  gases,  assumed  up  to  the  present 
by  all  physicists  to  be  exact,  viz. : — 

I.  All  gases  expand  to  the  same    extent  between  the  same 
limits  of  temperature. 

II.  The  rate  of  expansion  of  a  given  gas,  between  the  same 
limits  of  temperature,  is  independent  of  its  original  density. 

Must  these  laws  be  banished  from  science  for  the  future  ?  I 
do  riot  think  so.  I  believe  that  these  laws,  along  with  all  those 
which  have  been  discovered  for  gases,  such  as  the  Law  of  Vol- 
umes, etc.,  are  true  at  the  limit,  that  is,  that  they  come  nearer 
to  conforming  with  the  results  of  observation  in  proportion  as 
we  use  the  gas  in  a  more  expanded  condition. 

These  laws  hold  good  for  a  perfect  gaseous  state,  which  the 
gases  that  nature  places  before  us,  more  or  less  approach,  ac- 
cording to  their  chemical  characteristics ;  according  to  the 
temperature  at  which  we  study  them  and  which  may  be,  for 
each  in  turn,  more  or  less  removed  from  the  point  where 
change  of  state  takes  place ;  finally  and  chiefly,  according  to 
their  condition  of  less  or  greater  compression. 


150 


RESEARCHES  UPON  THE  GAS  THERMOMETER, 

AND  THE  COMPARISON  OF  THE  GAS  THERMOMETER, 

WITH  THE  MERCURY  THERMOMETER. 

BY  P.  CHAPPUIS. 

(Abstract) 

Travaux  et  Memoires  du  Bureau  International  des  Poids  et 
Mesures,  volume  6  (1888);  Archives  des  Sciences  (Geneve),  vol- 
ume 20,  pages  5—36,  153—179,  248—262  (1888). 


151 


CONTENTS. 


PAGE 

Gas  reservoir  and  baths     .            .            •            •            •  153 

Manometer           v  .            .            .            •            •            •  1** 

Barometer               ....••  155 

Mercury  Thermometers      ,            ...            .            .  155 

Average  Coefficient  of  Expansion  of  Nitrogen,  0  °— 100  °  .  156 

ditto                  Carbon  dioxide,     ditto          .  157 

ditto                           Hydrogen,     ditto          .  157 

Curves  showing  deviations  from  Mercury  thermometers     .  158 

Coefficients  of  Expansion  of  Nitrogen  and  Carbon  dioxide 

at  various  temperatures  between  W°  and  100°     .            .  158 


152 


RESEARCHES  UPON  THE  GAS  THERMOMETER, 

AND  THE  COMPARISON  OF  THE  GAS  THERMOMETER 

WITH  THE  MERCURY  THERMOMETER. 

BY   P.  CHAPPUIS. 

(Abstract.) 

IN  an  extended  memoir  Chappuis  describes  the  means  he  em- 
ployed in  his  attempt  to  determine  with  greater  accuracy  than 
had  hitherto  been  attained,  the  relation  existing  between  the 
rates  of  expansion  of  gases  and  of  mercury.  In  the  effort  to 
find  an  instrument  which  would  be  more  reliable  than  the  air 
thermometer  of  Regmiult,  he  made  use  of  a  gas  reservoir  the 
material  of  which  was  an  alloy  of  platinum  and  iridium  instead 
of  glass,  and  thereby  avoided,  in  part  at  least,  the  difficulties 
introduced  through  the  uneven  expansion  of  the  latter  sub- 
stance. This  reservoir  was  110  centimeters  long,  3.6  centi- 
meters in  diameter  and  had  a  capacity  of  a  little  more  than  a 
litre.  It  was  connected  by  means  of  a  platinum  capillary 
tube  a  meter  long  with  the  manometric  apparatus.  For  ex- 
periments at  0°  C.  and  below,  as  well  as  at  temperatures  up  to 
50°,  the  gas  reservoir  was  supported  in  a  horizontal  position  in 
the  inner  one  of  two  concentric  metal  troughs,  and  the  mer- 
cury thermometers  were  disposed  symmetrically  about  it.  In 
this  position  it  could  be  surrounded  with  crushed  ice,  with 
freezing-mixtures  or  with  liquid  baths  of  any  desired  tempera- 
ture ;  in  the  last  case  stirrers  driven  by  a  water  motor  kept  the 
liquid  in  motion  and  at  a  perfectly  uniform  temperature. 
Evaporation  with  consequent  temperature-variation  was  largely 
avoided  by  covering  the  troughs  with  a  large  glass  plate.  For 
a  vapor  bath  a  double-walled  vessel  was  employed  and,  some- 
what as  in  Regnault's  apparatus,  the  steam,  after  passing 
through  the  inner  vessel,  reached  the  condenser  by  way  of  the 
annular  space  beween  the  double  walls. 

In  Regnault's  constant-volume  air  thermometer  the  tension 
of  the  gas  was  measured  by  a  simple  manometer  open  to  the 

K  153 


MEMOIRS    ON 


air ;  consequently  a  baro- 
metric reading  had  to  be 
made  at  the  time  the  ver- 
tical difference  was  deter- 
mined between  the  two 
mercury  levels  in  the  mano- 
meter. The  number  of 
readings  involved  in  these 
pressure  measurements  ad- 
ded to  the  laboriousness  of 
the  work  and  to  the  liabil- 
ity to  error  in  the  results. 
Regnault  did  not  regard 
his  readings  of  heights  of 
mercury  columns  incorrect 
by  more  than  0.01  centi- 
meter, yet  he  considered 
such  an  error  always  pos- 
sible. To  increase  the  accur- 
acy of  the  tension  measure- 
ments was  Chappuis's  chief 


Fia.  1. 


154 


Fio. 


EXPANSION    OF    GASES 

care.  For  this  purpose  the  apparatus  was  so  arranged  that  but 
one  reading  was  necessary  to  give  the  total  pressure  exerted  by 
the  gas  in  the  reservoir.  The  platinum  capillary  tube  (c  in  Fig.  1) 
leads  from  the  gas  reservoir  through  the  close-fitting  steel  plug 
into  the  closed  chamber  shown  in  section  and  on  a  larger  scale  in 
Fiy.  2.  The  mercury  in  this  chamber  is  kept  just  in  contact 
with  a  fixed  pointer,  0.5  millimeter  long,  projecting  downward 
from  the  plane  under-surface  of  the  steel  plug,  by  raising  or 
lowering  the  mercury  reservoir  R  connected  with  the  mano- 
metric  chamber  by  a  steel  tube.  This  adjustment  can  be  made 
with  the  greatest  exactness  by  means  of  a  screw  movement 
attached  to  R.  The  difference  between  the  mercury  level  in 
the  closed  chamber  and  that  in  the  open  tubes  M,  M  and  R — 
which  are  all  in  communication  with  one  another — is  a  measure 
of  the  excess  of  pressure  in  the  gas  reservoir  over  that  of  the 
atmosphere. 

Dipping  in  the  open  well  Mis  a  barometer  B  attached  to  a 
movable  carriages  which  can  be  displaced  along  a  vertical  line 
by  means  of  the  screw-rod  s.  The  barometric  chamber  is  pro- 
vided with  one  or  more  black  glass  pointers  fused  to  the  side, 
the  tips  of  which  turn  downward  along  the  line  of  the  axis  of 
the  chamber  ;  by  means  of  s  the  barometer  is  raised  or  lowered 
until  the  mercury  meniscus  just  touches  the  tip  of  the  pointer. 
The  apparatus  is  so  constructed  that  the  barometric  chamber 
and  the  manometric  chamber  are  in  the  same  vertical  line  ;  hence 
the  total  pressure  upon  the  gas  in  the  reservoir  is  measured  by 
the  vertical  distance  between  the  menisci  in  B  and  n.  The 
tubing  of  which  B,  n,  M  and  M'  are  made  is  of  2.5  centimeters 
internal  diameter,  and  hence  the  menisci  show  little  curvature. 
The  position  of  the  pointer  in  the  manometric  chamber  with 
respect  to  the  scale  attached  to  the  support  being  once  for  all 
known,  a  single  reading,  that  of  the  pointer  and  meniscus  in  B, 
suffices  to  show  the  total  pressure  on  the  gas  in  the  reservoir. 

The  fact  of  the  exact  adjustment  of  all  these  levels  was  deter- 
mined by  means  of  cathetometer  microscopes  fitted  with  micro- 
meter eyepieces.  The  heights  were  read  off  on  a  metal  scale 
attached  to  the  manometer-support  close  to  the  manometer 
tubes. 

Eight  mercury  thermometers  of  hard  glass  were  used  :  four 

155 


MEMOIRS    OK 

were  graduated  from — 5°  to  104°;  the  other  four  from — 32°  to 
+  39°  and  from  95  °  to  103  °,  there  being  a  reservoir  on  the  stem 
between  39°  and  95°.  The  thermometers  of  these  two  kinds 
were  about  70  centimeters  and  54  centimeters  long,  respectively  ; 
the  divisions  corresponding  to  single  degrees  were  over  5.5  mil- 
limeters apart.  Prior  to  the  actual  determinations  most  care- 
ful calibration-tests  were  made  upon  the  gas  reservoir,  the  cap- 
illary tube,  the  reading  microscopes,  the  scale,  the  thermom- 
eters, etc.  The  coefficient  of  expansion  of  the  reservoir  was 
determined  with  another  tube  of  the  same  alloy. 

Nitrogen. — The  reservoir  being  filled  with  pure  nitrogen,  a 
series  of  determinations  were  made  of  the  pressure  upon  the  gas 
at  0°.  Of  the  19  measurements,  each  the  average  of  3-7  read- 
ings, the  highest  was  995.967  mm.  ;  lowest,  995.922  mm.  ;  mean, 
995.942.  These  measurements  were  made  on  various  days 
extending  through  two  months  and  a  half.  At  intervals  dur- 
ing this  period  the  pressure  corresponding  to  a  temperature  of 
100°  was  determined  ;  the  figures,  reduced  to  45°  latitude  and 
sea  level,  were : 

No.  Pressures  Corresponding  temperatures 

1.  4  readings  1358.057mm.  100.0548° 

2.  6  1357.424  99.8826° 

3.  6  1356.479  99.6212° 

4.  6  1356.795  99.7160° 

From  these  pressures,  assuming  the  mean  value  995.942mm. 
for  the  pressure  at  0°,  the  coefficients  deduced  are  : 

1.  0.00367482 

2.  0.00367471 

3.  0.00367468 

4.  0.00367442 
Mean,  a  =  0.00367466. 

Elaborate  comparisons  were  next  made  between  four  of  the 
mercury  thermometers  and  the  nitrogen  thermometer  at  15°, 
20°,  25°,  30°,  35°,  40°,  45°,  60.8°  (boiling-point  of  chloro- 
form) and  78°  (that  of  alcohol). 

A  second  series  of  determinations  of  the  gas  pressure  at  0° 
(the  room  temperature  being  lower  than  in  the  former  series), 
gave,  as  a  mean,  995.888  mm.  Comparisons,  on  the  assumption 
that  a  =0.00367466,  were  made  with  the  mercury  thermometers 

156 


EXPANSION    OF    OASES 

of  the  second  set  at  2.5°,  5°,  10°,  15°,  20°,  25°,—  4°,— 24°, 
— 20°,  — 15°, — 10°, — 5° .  The  results  of  these  comparisons  are 
shown  in  the  form  of  a  curve  on  page  158. 

Carbon  dioxide. — Twelve  measurements  were  made  (each  the 
average  of  4-8  readings)  of  the  tension  of  the  gas  at  0°,  and 
four  of  the  tension  at  100°,  as  in  the  case  of  nitrogen.  The 

values  deduced  for  a  were  : 

0.00372458 
0.00372483 
0.00372481 
0.00372486 

Mean,  a  =  0.00372477. 

Comparisons  were  again  made  with  the  mercury  thermometers 
at_i7°,-.lo0,  10°,  20°,  30°,  40°, 

Part  of  the  gas  having  been  allowed  to  escape  from  the 
apparatus,  so  that  the  pressure  at  0°  was  reduced  from  about  1 
meter  of  mercury  to  about  870  mm.,  nine  measurements  were 
made  at  0°  which  ranged  from  870.253  to  870.296  mm.,  and 
five  at  about  100°.  The  values  of  a  obtained  were  : 

0.00371629 
0.00371631 
0.00371646 
0.00371629 
0.00371635 

Mean,  a  =  0.00371634. 

Finally,  the  reservoir  was  filled  with  pure  hydrogen  obtained 
by  electrolysis.  Two  series  of  determinations  of  the  tension  at 
0°  were  made,  comprising  a  total  of  23  measurements,  each  the 
average  of  three  readings,  and  seven  determinations  at  100°. 
The  calculated  values  of  a  were  : 

0.00366271 
0.00366248 
0.00366225 
0.00366231 
0.00366256 
0.00366270 
0.00366269 

Mean,  a  =  0.00366254. 

Comparisons  of  the  readings  of  the  hydrogen-  and  mercury- 
thermometers  were  made  at  17  different  temperatures  between 
—24°  and  78°. 

The  curves  showing  the  deviations  of  the  nitrogen-,  carbon- 
dioxide-  and  hydrogen-thermometers  from  the  mercury-ther- 

157 


MEMOIRS    ON 


mometers  are  exhibited  in  Fig.  3.     The  maximum  deviations 
are  : 

For  hydrogen,  0.107°  at  40°, 

For  nitrogen,  0.097°  at  40°  , 

For  carbon  dioxide,  0.049°  at  35°. 

It  will  be  noted  that  from  about  65°  to  100°  the  value  of  a  is 
practically  identical  for  hydrogen  and  nitrogen. 


0.10- 


05- 


-20      -10       0 
—  O.°05 


—  Of  10  - 


FIG.  3 

The  coefficients  of  expansion  for  nitrogen  and  carbon  dioxide 
at  temperatures  ranging  from — 10°  to  100°  are  thus  stated  by 
Chappuis  : 

Nitrogen  Carbon  dioxide 

0.00367781  0.00373807 

7698  3538 

7625  3273 

7561  3019 

7506  2779 

7461  2558 

7426  2360 

2191 
2054 
1954 
1896 
1884 

In  the  case  of  carbon  dioxide,  the  change  of  the  coefficient  of 
expansion  with  change  of  pressure,  is  given  thus  : 

Initial  Pressure  Coefficient 

999.18  0.00372477 

870.28  0.00371634 

158 


Temperature 
—10° 
0  ° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

90° 
100 


EXPANSION     OF     GASES 


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28,  233-246  (1890). 

Melander:  Wiedermann's  Annalen,  47,  136-154(1892). 
Baly  and  Ramsay:  Philosophical  Magazine  [5],  38,  301-327  (1894). 
Kuenen  and  Randall:  Proceedings  of  the  Royal  Society,  59,  60- 

65  (1895). 
Leduc:   Journal  de  Physique,  [3]  7,  201-209  (1898);  Annales  de 

Chimie  et  de  Physique,  [71  15,  95-105  (1898). 
Leduc  and  Sacerdote:AnnaZes  de  Chimie  et  de  Physique,[7]  15, 

60  (1898). 

Harker  and  Chappuis:  Philosophical  Transactions,  194  A,  37-134 
(1900). 


160 


INDEX. 


PAGE 

A 
Air,  Coefficient  of  Expansion  of : 

Amagat,      •••.,..  11 

Amontons,      .        .            .           .           .  .  -   .;  30 

Bottcher  and  Wiebe,        .           .           .  .  .  13 

Callendar  and  Griffiths,  .            .           .  .  ..  13 

Dalton,                    .            .            .            .  .  .  go,  22 

Flaugergues,          .           .           .           .  . -v  .,.-  5 

Gay-Lussac,   .                   ^           .  , .  .  43 

Griffiths  and  Callendar,  .            .  .  ^  13 

v.  Jolly,       .           .           ;           .           .  ..  .  10 

Magnus,                  .           .           .            .  .  .  7 

Melander,    .           .           ,.          ¥           .  .  14 

Mendeleefif,             .           .            .            .  .  .  11,  12 

Priestley,    .           .           0           .           .  .  34 

Eegnault,    .            .V         .         81,  89,  95, 100,  126,  134,  136,  143 

Rudberg,     .          ..           .           .        ,   ,   ,        .  .  .  6 

Stewart,      .           .           .  .          .           ..  .  9 

Wiebe  and  Bottcher,        .           .            .  .  .13 

Air-scale  and  mercury-scale  of  temperature,  4,  104,  158 

Amagat,          .           ...  .  10 

Ammonia,  Coefficient  of  Expansion  of : 

Gay-Lussac,            .           .           .  .  .  46 

Priestley,     .           .            .           .  .  ,  34 

Regnault,    .           .           .           .  .  .  109 

Amontons,          .           .            .           .        •  .  .  .  30 

Andrews,             .           .            .           .            .  .  .  12 

Argon,  Coefficient  of  Expansion  of:  Kuenen  and  Randall,  14 

B 

Baly  and  Ramsay,        .           .           .           .  .-  .  15 

Bettancourt,        .           .           .           .           .  .  .  27 

Berthollet,           .           ...           ^           .  .  .  34 

161 


INDEX. 

Biot:  Traite  de  Physique,       .  .  .  .     4,  51,  74,  106 

Bohr,        .  . 15 

Bottcher  and  Wiebe, 13 

Boyle's  Law,  Variations  from,  .  .    8,  10,  137,  144 

C 

Callendar  and  Griffiths,  .  .  .  .  ;  13 

Carbon  dioxide,  Coefficient  of  Expansion  of: 

Amagat,  .  .  .  .  ...      10,  11 

Andrews,          .  .  .  .         v .  .  12 

Baly  and  Ramsay,      .  .  .  .  .16 

Chappuis,          .  .  .  .  .  .    13,  157 

Dalton,  .          -.'          .  .          ,;'          .  21 

Gay-Lussac,      .  .  *  .  .  45 

v.  Jolly,  ...-:         .        •   .  '         .  .  .  10 

Magnus,  .  .  .          -.  .     •  -«  .  7 

Melander,          .  .  .  .  .  .  14 

Mendeleeff ,       .  .  .  .  f  .  12 

Priestley,          .  .  .  v    ^   .  .  .  34 

Ramsay  and  Baly,       .  .  .  .  .  16 

Regnault, 109,  143 

Carbon  monoxide,  Coefficient  of  Expansion  of : 

Regnault,          ......  109,  143 

Chappuis,  ...  .  /  .  .  .    13,  151 

Charles,  ' ;. 37,  60 

Constant  Pressure,  Coefficients  at :  Causes  of  differences,          147 

Cyanogen,  Coefficient  of  Expansion  of : 

Regnault, 109,  143,  147 


Dalton, 3,17,22,59,71 

Davy, 124 

Deluc, 32 

Dulong  and  Petit,          .  .  .  .  .  4,  23,  103 

Duvernois  and  de  Morveau,  ...  3,  20,  34 

F 
Flaugergues,      .......  5 

G 

Gay-Lussac,       '.  .  .  .  .3,25,48,51,65,71,101 

Gilbert,    .          \  .     •   .  71 

162 


INDEX. 

Glass,  Coefficient  of  Expansion  of,    .  .     5,  21,  57,  79,  84,  103 

Griffiths  and  Callendar, 13 

Guyton  de  Morveau,     .  .  .  .  .  .  3, 20, 34 


Harker  and  Chappuis,             .....  13 
Helium,  Coefficient  of  Expansion  of: 

Kuenen  and  Randall,            .            .           .  .  14 
Hydrobromic  Acid  gas,  Coefficient  of  Expansion  of: 

Mendeleeff,        .....  12 
Hydrochloric  Acid  gas,  Coefficient  of  Expansion  of : 

Gay-Lussac,      .           .        •    .           .  .  45 

Priestley,           .           .           .           .  .  34 

Regnault, 109 

Hydrofluoric  Acid  gas,  Coefficient  of  Expansion  of : 

Priestley,           .           .          . ,.,.         .  .  34 
Hydrogen,  Coefficient  of  Expansion  of : 

Amagat,      .            .            .            .  .      10,11 

Baly  and  Ramsay,            .           .           .  .  15 

Chappuis,   .            .            .            .           .  .13,  157 

Dalton,        .            .            .            .           .  .  21 

Gay-Lussac,           .           .           .  .  43 

v.  Jolly,      .            .           .           .            .  .  10 

Magnus,      .           .          %            .            .  .  7 

Melander,    .                       .           .           .  .  14 

Mendeleeff,             .           /          .  •     ' .'..,  .  12 

Priestley,    .            .           .         .  .           .  .  34 

Ramsay  and  Baly,            •.           .           .  .  15 

Regnault,    .           .            .         . ' .            .  .  109, 143 

Hydrogen-thermometer,  Coefficient  of: 

Expansion  used  by  Regnault      v           .       >  .  9 


v.  Jolly,  .  .  .  .  ....      9,  12 


Kajander  and  Mendeleeff,        ...           .  .  11 

Kelvin,  Lord,     .            ...           .           .           .  .  9 

Kuenen  and  Randall,    .            .           ...  .  14 

163 


INDEX. 

L 

Lahire,     .                       .  .  .  .  .  .           31 

Law  of  Expansion  of  Gases : 

Amontons,        .  .  .  .  .  .30 

Dalton,  .           .  .  .  .  .  21 

Gay-Lussac,      .  .  .  .  .  ,           48 

Regnault,          .  .  .  .  .  -.150 

M 

Magnus,     .  .  .  .  .  *  ^  6,12,144 

Manometer  of  Chappuis,         '  .;          .:          «  .  .         155 

"  v.  Jolly,  .  .        .,  .  .  '       •  .  .  9 

"  Regnault,         .    .  .        .   .  .  90, 97,  127,  130 

"  Rudberg,         '.  ,  .  ;  .  .  69 

Mariotte's  Law,  Variations  from  Boyle  and,  _^«        10,  137,  144 

Mayer,  Tobias,      .  .  .  .  .        '   .  .  60 

Melander,  .        .  .  .  .  .  .  ;  .  14 

Mendeleeff,        ~Y          .  .  ...  ,  .     11,16 

Mercury,  Coefficient  of  Expansion  of,  ...     4,  103 

Mercury -scale,  Comparison  of,  with  gas-scales,       .  .      4, 158 

Moisture,  Effects  of,  .  .  .3, 19, 31, 37, 53 

Monge,       ........  34 

de  Morveau  (Guy ton),    ......  20 

N 
Nitrogen,  Coefficient  of  Expansion  of: 

Amagat,         ......  11 

Baly  and  Ramsay,   .....  15 

Chappuis,       .  .  .  .  .  .    13,  156 

and  Barker,      ....  13 

Gay-Lussac,  ......  44 

Harker  and  Chappuis,        ....  13 

v.  Jolly,          .           .                       .           .           .  10 

Priestley,       .....*.  34 

Ramsay  and  Baly,   .....  15 

Nitrous  oxide,  Coefficient  of  Expansion  of : 

Dalton,    .            .            ...            .            .  21 

Gay-Lussac,       .           .           ...           .  46 

Priestley,           .           .           ...           .  34 

Regnault,  .  .  .  ...  109, 143 

Nuguet,      .           .           .           .           .           .           .           .  31 

164 


INDEX. 

O 
Oxygen,  Coefficient  of  Expansion  of: 

Amagat,   .......  11 

Baly  and  Ramsay,      .....  15 

Bohr,     .......  16 

Dalton,  .           .            .            .            .            .            .  21 

Gay-Lussac,     ......  43 

v.  Jolly, 10 

Priestley,          .            .            .            .                       .  34 

Eamsay  and  Baly,     .           .           .           .           .  15 

Regnault, 109 

P 

Pressure,  Effect  of  decreased,  on  the  Coefficient  of  Ex- 
pansion of  Gases : 

Air,        .            .            ,            .            ,,          ; .,'          .  14,  126 

Carbon  dioxide,          .           £.>        .            .            .  14,  15 

Hydrogen,        .            .  .         .            .        ^  .            .  14, 15 

Nitrogen,          .            .    •      '•  „           .            ..           .  15 

Oxygen,            ,           .            .            ,            .            .  15 

Pressure,  Effect  of  increased,  on  the  Capacity  of  glass 

bulbs,         ..           .           .                       .           .           .  132 

Pressure,  Effect  of  increased,  on  the  Coefficient  of  Ex- 
pansion of  Gases : 

Air,        .            .            .            .            .             11,  12,  134,  143 

Carbon  dioxide,          .            .            .11,  12,  136,  143,  157 
Hydrogen,        .....         11,  12,  143 

Nitrogen,          ......  11 

Oxygen,            ......  11 

Preston's  Theory  of  Heat,         .....  73 

Priestley,  ........  33 

R 

Ramsay  and  Baly,           .  ~          .            .            .            .            .  15 

Randall  and  Kuenen,      ......  14 

Recknagel,            .            .            .            .            .            .            .  9 

Regnault,              3,  7,  12,  63,  120,  121,  153 

RoiorRoy, 19,33 

Roscoe,       .                       .           .           .           .           .           .  3 

Rudberg,               .        '    .           .            .            .           .            .  4,  5,  65 

165 


INDEX. 

S 
de  Saussure,         .  .  .  .  .  .  .33 

Siljestrom,  .......  16 

Stancari,    . 32 

Stewart,     ........  9 

Sulphur  dioxide,  Coefficient  of  Expansion  of : 

Amagat,  ......  10 

Gay-Lussac,      .  .  .  .  .  .  .        46 

Magnus,  .....  ..  7 

Priestley, 34 

Regnault,  .  .  .  .  .     109,143,146 


Temperatures,  Coefficients  of  Expansion  of  Gases  at  high,  10 

"                      "                       "  "very  low,             9 

"              on  gas  and  mercury-scales,  .  '?        4,  104,  158 

V 

Vandermonde,      .           ;           *           .           .  .           .?        34 

Vapors,  Expansion  of,    .           .           .           .  .           .    47, 150 

W 

Water- vapor,  Effect  of,  in  gases,        .           .  .3,  19,  31,  37,  53 

Wiebe  and  Bottcher,      .           .           .           .  .         , .           13 


Ziegler,      »  .  ,. 27 


166 


Scientific   Memoir  Series 

EDITED  BY  JOSEPH  S.  AMES,  Ph.D. 
Johns  Hopkins  University 


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